Personally, like you said, i think it was a lack of heat that caused the regurg. Basically, the food just rotted in his gut. It's your call but me personally, i wouldnt take the blood in to the vet. The only thing the vet could do that would give answers would be a fecal or blood work. Blood work is expensive. I think when i had Harley's blood work done, it cost me around $150 or $200. Fecal floats are cheap. My vet charges like $30 for one. If you are a regular at the vet, he/she might work with you on the price if you explain you're in a bind. When i took Rosey in for her sinus infection, it came at the worst possible time for cash. I told my vet and she basically just charged me for the meds and office visit and gave me a pass on the culture of the liquid in her nose.
But anyways, i would for sure take the BP in as you said it clearly has an RI. But like i said, the blood, i would probably pass on it and raise the temps like you did and give him at least 2 weeks before trying to feed him again. Regurg is really hard on their system and after that, he will need time to rebuild his stomach acid supply, otherwise he could just regurg again and lose even more stomach acid and fluids. And i would mix in some unflavored pedialyte into his water which will help replenish electrolytes and stuff he lost from puking so much.