I wouldn't think the eye would swell because of the heat. It would be far more likely that your cat was bitten or stung by something or it could be caused by the poor air quality - which is, I suppose you could say, a product of the horribly hot weather we're having everywhere right now. If it continues, you might want to put cool compresses on it to see if that helps bring the swelling down and take him to the vet to have it looked at. Anytime the eyes are involved, I personally feel having the vet check things out is prudent since vision is so important and fragile.
Please let me know if I can help further.