You might want to think about setting in other novels and plays etc and compare them to this novel. Clearly the intense heat acts in The Great Gatsby as a kind of revealer if you like. When it is so sweaty and humid, the masks of respectability we place on top of our real, chaotic and unprincipled selves slip somewhat and we show ourselves for who we really are. This is essentially one of the major themes of the novel - the narrator is given access to this privileged jazz-age world of money and dubious values and, thanks to the weather, is able to see it for what it really is...
The "sweltering summer heat" is uncomfortable and, as noted above, sets everyone on edge. That's exactly the tenor and tone of this encounter. I guess if you're looking for an actual literary term, I suppose it's a bit metaphorical--just as there was "sweltering summer heat" on that day, there was plenty of heat both at the house and the hotel--and even at Wilson's garage. Those are the three stops the group makes through the course of this day. A married couple, a few friends, and two lovers is a combustible recipe for disaster--which is how the day ends.
Well, it's not quite alliteration as one usually needs at least three repetitions of the consonant to be considered an example of the term. However, it does slide on the reader's tongue like a droplet of sweat down the back of the character who suffers from the heat. Think, also, that heat always effects one mood. Heat causes not only characters, but the readers who put themselves in the characters' shoes to react in "hot" attitudes. We are less tolerant, patient, rational when we are overheated. We are more likely to be impulsive, angry, rash, and irresponsible when we are uncomfortable...especially in the company of those we already dislike and distrust. This is the case in much of the book where Tom, Daisy, Tom's lover and her husband, and Gatsby are concerned.
This is a good jumping-off place, and I feel certain others will add to what I've started here for you. Good Luck!