B.W.
Pretty common, I had sweaty babies too. Both boys would sweat their little behinds off in the car seat as babies! If he starts crying, that will make him sweat too, so it may be he's not initially sweaty, but when he starts crying, he gets sweaty.
If you have a car that doesn't have seperate rear cooling vents, point the vents in the middle of the dash (between the drivers and passengers seats) up towards the ceiling to bounce the AC to him. Also when we lived in TX I bought a small clip on fan, it was one of those with the foam blades, and it took two AA batteries, and had a clip so I clipped it ot the headrest and that helped to keep the AC blowing back onto him after it was bounced off the ceiling. I had a small sports car then.
We live in Minnesota now, but it still gets hot and muggy in the summer. I used that fan again with our youngest, he rear faced until he was 3, and that fan came in handy every summer he was rear facing.
Keeping him cool by light layers, dressing him in cotton, bouncing the front vents to the ceiling to hit him, a small fan that clips on (make sure it clips to something for safety) will all help.