We weren't given any pain meds. I am so nervous now. How do I check his temperature? Also, is shivering normal? He is shivering quite a bit, but again, still eating and drinking. How do I know if it is infected? Sadly, I have never experienced any of this, so I guess I am clueless and I would rather ask Savannah parents over normal cat parents...although I know ppl say Savannahs should be treated like normal cats.
Get a good digital thermometer at Walgreens/CVS/Walmart, maybe one that reads ~10sec and not ~30sec, make sure the tip is round and smooth

. Usually they say anal approved, etc. Get some Vaseline. Lube up its tip just a bit so it doesn't hurt your cat (but not too much as the Vaseline could serve as a temperature insulator a bit). And up the butt carefully and slowly so the metal tip and maybe 1/8-1/4" plastic is in, and take a reading until steady state temp reached and it beeps. He may make a meow or two, that's normal. Might be best to have you and someone else present.
In terms of the neutering, Shango did shiver a little bit in the beginning, it's not necessarily normal though. In terms of infection detection, that's a bit tougher maybe. If it's red and swollen after a day or two and he's running a temp (my breeder says above 101F, my vet says above 102.5F for a mild fever), then go see your vet for at least a look. Mostly ensure he's hydrated. From everything I understand, post neutering infections are not that common. Shango got one, but if you read most posts here, neutering has gone pretty well in general. My vet and I suspect he got it via licking, going to the bathroom or even just sitting. Shango was fine day1, and it wasn't until late day2 that I think it got infected. Hope this helps and wishing your cat a speedy recovery! ..dj