(The rest of the posts in this series can be found here.)
Aquinas thought a temporally finite universe could not be demonstrated by reason. The kalam cosmological argument, by contrast, argues that a temporally finite past can be demonstrated via both a priori and a posteriori arguments.
Craig has offered two a priori arguments and two a posteriori arguments for the finitude of the past. The first argument attempts to show that actually infinite sets of things cannot exist in reality, and so the set of past events cannot be actually infinite. The second argument attempts to show that even if an actually infinite set of things could exist in reality, its members could not be successively traversed. But if not, then since the members of the set of past events have been traversed -- after all, here we are -- that set must be finite.
According to the first a posteriori argument, the Big Bang theory of the origin of the universe implies an absolute beginning to spacetime, in which case the past is finite. And according to the second a posteriori argument, the second law of thermodynamics implies an absolute beginning. For since the universe is winding down energywise, it must've been wound up, with an initial, massive imput of usable energy.
So the universe must've had a beginning. And since all things that begin to exist (note the qualification) have a cause of their existence, the universe had such a cause. Now there are two sorts of causes: personal and impersonal. But the cause can't be an impersonal cause, for any such cause must be in a state of quiescence or activity. But neither disjunct will do. For if the cause were in a state of dormancy, then since no events are occurring in that state (remember, we're talking about the cause of the first moment of time, and so no events can occur "before" the first event), it would remain in a permanent state of stasis. On the other hand, if the cause were in a state of activity, then the universe would be eternal. For the effect of an impersonal cause occurs as soon as such a cause is present. And if that's right, then if the cause is eternal, then the effect is eternal. But we've just seen that the effect is finite. Therefore, the effect -- the universe -- did not arise from an impersonal cause, whether active or quiescent.
So an impersonal cause of the beginning of the universe is out. But a personal cause can play the role here. For it can (in principle at least) exist in a state of eventless quiescence and spring into action with a spontaneous, libertarianly free act of the will. Therefore, the universe had a beginning, and it was caused by the spontaneous, free act of a person of some kind. But since it is the cause of spatiotemporal, physical reality, it must be a timeless, immaterial being of immense power. And this, as Aquinas would say, we all call 'God'.