It is hard to avoid uncertainties in the various related scenarios of this general case, but we will try to give the general guidelines.
Rishonim struggle with the question why one doesn’t make a birkat haTorah each time he learns, like he makes a beracha each time he eats in a sukka. The standard explanation is that Torah study is an ongoing mitzva and experience that does not lend itself naturally to interruptions.[2] Most Rishonim rule that breaks that would require a new beracha are possible, especially if one takes a significant nap during the course of the day.[3] However, there are opinions that hold that no break during the day stops the efficacy of the morning birkat haTorah, which was intended to last until the end of the person’s day. The minhag is to employ the concept of safek berachot l’hakel,[4] which is the second and conclusive opinion in the Shulchan Aruch,[5] and not to make another beracha.
However, after going to bed at night (not merely putting one’s head down on a table), almost all agree that the day’s learning is over and if one wakes up and wants to learn later at night, he must make a new birkat haTorah.[6] The question arises, though, whether going back to sleep before the morning would mandate another birkat haTorah in the morning. It appears that those who don’t require a new birkat haTorah would halachically consider a second period of sleep like a nap. The Mishna Berura[7] explains that, according to the Shulchan Aruch’s approach, one should not to make a new beracha after a second sleep because we assume that a person would intend that the beracha he made during the night should be effective through the next day.
The Minchat Yitzchak[8] uses the idea of the impact of one’s intention when making the beracha to come to a different recommendation in a similar case. He was asked about those who regularly take a long nap in the beginning of the night to enable them to stay up late learning. He suggests that they have in mind in the morning to have their beracha last until their main sleep of the night, not to have it broken by the nap. Rav Mordechai Willig not only concurs but goes as far as to say that this need not be intended cognitively but is an assumed intention. (Clearly, not all agree with this cogent position.) Certainly, in the case you discuss, where one goes to sleep for the night and wakes prematurely, he should make the beracha before learning at night.[9]
Be aware of the fact that it is generally legitimate (if not recommended) to make a birkat haTorah after any significant nap.[10] If one believes, but is not absolutely sure, that he should say a birkat haTorah, he should preferably make only the beracha of “asher bachar banu…” and not “asher kideshanu…”[11]