The 'heat' from the exhaust flame (unburnt fuel on decel?) is likely just oxidation of the adjacent painted surface and would NOT be comparable to a bake oven where the part is subjected to a continuous level of high heat over time. 1st step is to ensure that physical part damage has not occurred to your rear fasica. You can tell if there is physical damage - e.g. part has distorted/warped or the surface has very small bubbles in the part surface (degassed).
The original front and rear GT fascias were molded, then shipped to an intermediate supplier who painted them with a red spot primer and then hand sanded. Fascias were then painted along with the car to gain color match, but were placed on separate racks, so that the fascias could be fully supported. If the fascias were not fully supported in the bake process, the high temp environment (+275F) may cause the parts to incur deflection/distortion.
As to painting, or OE repair, one of the key areas for consideration is your painters process. If they are using a similar high heat oven to cure the paint, you may inadvertently incur degassing of the part. This would happen when your painters oven temp/time exceeds that where the original part was molded and painted - and it does happen, as the OE process does have variability in time/temp and there is no way to know the exactly parameters where under which you specific part was mf'd and subsequently painted. You'll know if/when you exceed the time/temp as you will see the small bubbles described above.
A shortcut might be to have the painter look at some lower temp processes where part integrity is not compromised (<120F). Another suggestion might be to contact someone like the GT Guys who have significant experience with refinishing GT parts. I don't know what they using (paint or process) but the quality of the finish paint work out of their shop is comparable to OE.