Critical thing is that the carcass temperature shouldn't go up, but steadily come down to below 7 degrees. Rapid chilling affects the meat and there's lots of anecdotal info out there about this but little definitive. This paper provides some context:
If I'm going to be out all day away from my chiller I put gralloched chiller-ready roe and muntjac carcasses into a large Homebase black storage container (blood
egg-box at bottom) into which I've fitted a large 12v cooler box lid. This won't dramatically chill the carcass but importantly, but it stops temperature build-up in the closed box and keeps flies and other pests out, permitting a slow reduction in carcass temperature. For larger species, I cover the sled with the animal in it and turn the car's rear chiller up to max (fortunately my DS has 2 air con units!). This is only for a couple of hours but as you'll read on other threads on here you can use frozen water bottles inside the chest cavity to keep it cool whilst you transport it to your facility.
There is no set answer here and
your HACCP should reflect your modus operandi and have appropriate mitigations.