Actually there may not be a big heat difference between a hill climb and an autox. My car was running a little hot during this past autocross, and i was only running a bit hotter during the VC Hill climb (much more air flow to cool things down)
I was coming off the autoX at 3 o'clock, and maybe 2:30 at the VC (maybe 2:45 ish?)
depends on Which hill climb, and if the temps(weather) are comparable
I didn't know that under tray was so important either.. mine has some cracks in it and some pieces misses (dirt road adventures) maybe i should duct tape those up (since its acting like an air duct of sorts)

come to think of it i never ran hot at all during AutoX , back when my tray was in perfect shape ...