The exhaust and the muffler are, the frame and body get hot but not nearly that hot, heat shields and air gaps help keep them much cooler. They are probably not much hotter than the surface of the car on the hotest day of the year. The animal would have to stand still long enough on a hot surface to stick and the pain reflex would put a kabash on that fast enough. If it just bounced onto the muffler or evne the engine it would not have enoguh time before it bounced off to really stick. (I've accidentally touched them in the past, try the inner bicep skin on a header some time; you will flinch real fast!
How many skin cells do you think became attached to the header from that quick brush?
I'm not saying the squirrel would stick to the undercarriage like it was made of velcro.
I used to park my car in a private lot-one night I pulled in and hit a cat--I think he was running and I drove over him not ran over with the tire--I heard 2 thumps and braked and when I got out the cat was running away low to the ground
The next day I drove to work and could smell hair burning and looked under my car((91 Camaro)) and could see nothing
When I got home my mom asked if I had seen Mrs Kozacks cat and I told her what had happened---poor fella was in the animal hospital with burns
He had fur and skin burnt off from the 2 quick thumps I had heard--One part on the top of his back was almost to his spine and the second area on his back top leg area was mainly fur gone and lightly burned
As for me myself--One time while in Maine for a funeral my muffler fell off(pipe not unit) and I was trying to hold it up with a coat hanger that I had gotten from a restaurant--I must have burnt myself about 10 times till I got it to where it wouldn't drag on the ground--and your right I flinched,swore and stuck the burnt area in my mouth
Well I still ended up with angry red welts-- the top part of my left hand has a scar from where it touched,I actually got to watch my skin bubble.
So I guess with all that what I was trying to say is that I didn't expect the whole squirrel to be under there but rather skin cells of the squirrel