If you use anything more than a hairdrier, you run a good chance of deforming the body. Even a heat lamp can be enough to deform it. I have used hairdriers to dry coats of paint on lexan bodies with no problems. You do not want to hold it in one spot too long.
As far as painting, you really dont need to use primer on it unless you have done some fiberglass work to any of the parts. 1st I use a red scuff pad on the whole body to get rid of any shiney on it. Then I use dupont sealer, and the follow with the base color and then clear. Ive never had any problems. Even crashes and the stuff holds up pretty well. I just did another 03 cobra body, but I made a big cowl hood for it. I have yet to paint the hood on it. Here are some pics of the black one I did and then the yellow one with the unpainted hood. When I did the black car I baked it(after the clear) in the paint booth for like 6 min @110, but I was scared it would get deformed. On the yellow on I just used some PPG fast clear(air dries in 7 min) I wouldnt use anything to bake them though, too risky.
I will be painting the hood at work on monday. I was going to use the 04 cobra Mystic color, but I wanted the car to be bright to see it at night.(which is usually when we run them)