Studiousness, or studiositas, is, according to Aquinas (ST 2-2.166), a potential part (or adjunct virtue) of temperance. As the name of the virtue suggests, its act is study, which Aquinas glosses as "an intense application of the mind to something". It is therefore a virtue concerned with the direction of cognition (cognitio), or knowledge in a very broad sense of the term. The reason the virtue is needed is that we do not merely happen to be acquainted with (cognoscere) things; we have a drive to it. This needs to be moderated, and it is this moderation that associates studiousness with temperance as a potential part.
Studiousness is, further, a subjective part or particular version of the virtue of modestia, the understanding of which Aquinas gets from Cicero. Modestia concerns itself with the way (modus) things are done; different subjective parts of it concern different kinds of inclinations that are expressed in ordinary, everyday life, whether it be our drive toward excellence (humility) or our tendency to play (eutrapelia) or, as in this case, our thirst for things that contribute to knowledge.
Despite the fact that it might not sound like it, studiousness is very much concerned with our use of our bodies. We are not pure minds, so even though we have a natural desire to know things, there is a 'drag' on this desire arising from the bodily desire to avoid the difficult and unpleasant. In order to develop the virtue of studiousness, we must restrain the former so as to study the right things in the right way in the right order, and we must overcome the latter so as to follow through. This is the reason why Aquinas insists on study as the intense or vehement application of mind: it must have the force to overcome the trouble of learning. Thus the two vices opposed to the mean of studiousness are curiositas, which tends to pursue knowledge with a disordered object, and desultoriness or languor in learning.
Studiousness is thus heavily concerned with eliminating attempts to cut corners in the application of mind, attempts to get magical solutions and easy answers that don't involve the intellectual work appropriate to what we are trying to know.