Aquinas rejects the notion that the damned are tormented solely by fire, arguing that a variety of tortures will be employed. The term ‘fire’ is prevalent in scripture to describe the intensity of the pain, not the specificity of the torture. Eternal suffering, likened to the horror of being burned, is inflicted by torment ‘in many ways and from many sources’ and without respite. Indeed, hell will be so arranged ‘as to be adapted to the utmost unhappiness of the damned,’ and there will be, he argues, just enough light to perceive ‘those things which are capable of tormenting the soul.’ (Summa Theologica Suppl. Q. 97, Art. 5) One will, for example, see the corporeal fires and smell their stench as they burn one’s corporeal body. This never ending fire, Aquinas believes, is sustained not by fuel but by the very breath of God.
One of the difficulties of talking about the medieval notion of hell is that all the most obvious words for talking about hell in English are filtered through Calvinism, first, and, beyond this, associated with fire-and-brimstone preaching and comic depictions of hell. We have to be careful about the assumptions we bring into the discussion. For instance, we have to be careful when Aquinas says something like, 'That fire will be of the greatest heat'; 'heat', like 'fire', is a technical term in medieval thought, and the term 'heat' indicates the property of very intense activity, not necessarily heat of the sort that feels hot. Or, another example, when medieval theologians talk about the 'suffering', passio, of hell or purgatory, they mean the state of undergoing the action of an external agent, not intense pain; souls in hell or purgatory are dominated by outside forces in ways that souls in heaven are not; that was, incidentally, what 'suffering' in English originally meant, and still occasionally means in various older expressions. I have found that people have difficulty grasping these kinds of shifts. And all the talk of fire is not arbitrary. Aquinas notes that Jesus himself talks about the fire of hell (Matthew 25:41); he argues that there are insuperable difficulties with taking this fire to be purely metaphorical, however different it may have to be, or merely imagined. So the question becomes: What is actually going on in the penalty of fire?
(There is another issue we have to be careful with. Clark is basically flipping through the Supplementum in his summary above. The Supplementum, however, is not strictly by Aquinas, although it sort of is. The Summa was never finished. It stops in the middle of a topic in Part III. The Supplement was made to complete the course of topics in the Summa; it is a digest of questions and answers drawn primarily from Aquinas's Commentary on the Sentences by someone other than St. Thomas himself. This creates a number of issues. Obviously there are the problems arisign from the fact that the condensation of one work by someone other than the author might sometimes be potentially misleading as to the author's actual view. Also, the Sentences Commentary is Aquinas's earliest work; it was chosen as the source of the Supplement not because it contains the final views of Aquinas on any subject but because it is quite comprehensive in the topics it covers. For instance, the question on the sacrament of matrimony in the Supplement is certainly not in every respect what Aquinas would have written had he ever written it, because Aquinas's views on sacramental theology changed quite a bit between the beginning of his career and the end, and we are missing what would have been the most important element of Aquinas's discussion -- how, exactly, he would have applied the instrumental-cause account of the sacraments to matrimony. The discussion of hell in the Supplement, in short, is a condensed digest of the very earliest discussion of hell we have from Aquinas, made by someone other than Aquinas, and not necessarily with any regard for Aquinas's mature views, whatever they might have been. There are in fact points in the sections on hell, like the discussion of the demerits of hell, where we have good reason from other passages in the actual Summa to think that Aquinas would have answered the question differently than what we get in the Supplement. But this is not hugely important for this particular topic, as far as I can see. I will in what follows chiefly stick to what we find in the Supplement.)
The penalty of fire in hell in Aquinas's view is not a torment of destruction -- the damned are incorruptible. They don't burn in our usual sense, because burning is destruction by fire, and they are indestructible. Aquinas is very clear about this. He actually has some difficulty handling the weeping attributed to the damned because of it -- crying as we think of it requires destruction and generation, and there is no destruction or generation in the age to come. (He holds that when we say they weep, we mean that they have some of the physical turmoil we associate with weeping, not that they cry tears.) So the damned cannot be physically harmed by the fire. What is more, the fire Aquinas has in mind is not what we think of as fire. It is not fire in the sense that immediately pops into mind. I've noted before that we tend not to grasp what medieval thinkers are talking about when they talk about the elements, and it's too long to go into with proper precision here. But a brief, crude summary: pure elemental fire is that in the world which at the most fundamental level tends to act vehemently on other things and resist change by its environment. (What we think of as fire is a mix of elements that has some preponderance of elemental fire over the other elements.) It is the most active thing in the physical universe, and the thing that is hardest to turn aside.
Aquinas says he doesn't know exactly know what the fire will be, materially speaking, only that it will be genuinely classifiable as fire, in medieval terms, whatever strange properties it might have. If it's some particular form of pure elemental fire, then it's just a variety of our kind of fire; but he also allows the possibility that it could be some strange kind of fire capable of subsisting without transformation in something other than itself. In any case, it's misleading to say, "This never ending fire, Aquinas believes, is sustained not by fuel but by the very breath of God." What Aquinas actually says is that, given that it is never-ending fire, it cannot be sustained by fuel but must be such that it does not need to be sustained, just being inexhaustible by nature; the point is that it is misleading to compare it to fire in our sense. Fire in our sense (and again, 'our sense' here is the medieval sense) has to be introduced into a body by elemental transformations, and to keep it in a body requires continual elemental transformations. But the fire of hell, being never-ending fire in an incorruptible body, can't be sustained by continual elemental transformations; it just has to be never-ending by the nature God gave it. The "breath of the Lord" is, of course, from the prophet Isaiah (30:33); Aquinas interprets this to mean that the fire in question was originally made by God, not that God's breath is a continual blast furnace, as Clark's overly condensed summary makes it sound.
What the fire of hell does is not harm or destroy but constrain. Since it is hyperactive and cannot be turned aside, the damned just have to go along with what it does whether they want to do so or not. The torment of hell is in Aquinas's first and foremost a penalty for the will. To be punished for being damned is to be placed in a universe that refuses to let you do what you want. To be punished for being damned is to be subordinated to other things, things less noble than you are, like mere fire, that nonetheless at least behave as they should. This is actually one of the reasons why medieval thinkers tended to be more impressed by the image of fire as a punishment for the damned than other images: the damned fail to act as they should, so they are punished by means of something lower than them that consistently acts as it is supposed to, even when other things try to prevent it. (Actually, that's one reason why the fires of purgatory also struck the medieval imagination: the souls of purgatory, on their way to heaven, endure a penalty of fire, as well, and with similar symbolic appropriateness: they wavered due to their environment, and pure fire is unwavering. The patient souls of purgatory have to learn to be as pure and unwavering in the goodness of their nature as fire is pure and unwavering in the goodness of its own.) There is also, in Aquinas's view, a bodily penalty, but it is not burning-and-stinking, both which are inconsistent with the fact that the body of the damned is incorruptible, but 'commotion', that is some kind of physical activity deriving from the action of fire in constraining the will.
All of this obviously depends on medieval physics in various ways; Aquinas is very careful to make the assumptions that would have been most secure, and even then only follows them to the extent that is strictly required, and explicitly marks a number of things as simply unknown, but, of course, no amount of care in the use of the medieval theory of the elements could completely survive the (at the time) unforeseeable collapse of the medieval theory of the elements, just as it is impossible that an argument or position depending on the most secure claims about gravity we have could remain completely intact if it turned out five hundred years down the road that gravity is actually something radically different from anything we were taking it to be. What Aquinas is doing is taking Jesus seriously when he says 'fire' and asking what fire is that would make it suitable for Jesus to mention it in this context. (And it is worth keeping in mind that the same issues that come with interpreting Aquinas when he talks about fire come up when interpreting Jesus when he talks about it; just because Jesus says 'fire' does not mean that he is drawing on the same assumptions about what fire is that we are. In fact, we can pretty much guarantee that he is not. This is not a mere question of whether the term should be taken literally or metaphorically; what counts as taking fire-terms literally has itself changed over the past two millenia.)
Whether Aquinas's actual view would still, in Clark's view, be suitable to Clark's purpose -- which is to argue that the medieval conception of hell is inconsistent with the goodness of God -- I don't know. But it is an error to think of it as a "medieval torture chamber view of hell", as Clark does.