How scary! Yeah that sounds like heat exhaustion to me. I usually carry Uni over the black top but let her walk on the white sidewalks. I usually open the car door and hold Uni with my left hand, and kind of halfway go in the car and turn on the car and blast on the a/c and wait a few mins before I put Uni inside. Often if we are at home or leaving the shop, she won't even jump up into the car until she knows the ac is on and the car has kind of cooled down. Then even when we are on our way, she liked to hog the a/c vents.
I'm glad Riley's doing better.