I use one at El Mirage, but it is not permanently mounted in our roadster. Since we anticipate our run being no longer than a minute, we have the ice chest sitting on the tonneau (sp?) cover on a towel so it doesn't scratch anything. I suit up and get in (I usually suit up early with the vest because it is like a little piece of heaven on those 100 degree days) and finish belting and putting on my helmet/gloves. We keep the system hooked up until the starter has checked my belts, marked my run sticker and given me the go ahead. Then we pop the quick release valves and Scott takes the ice chest to the chase vehicle, and away I go. No additional weight added to the car and no having to worry about mounting. The suit stays very cool till the end of the run.
I know the roadrace guys mount theirs, but since we don't need it for a 45 minute race, we don't. You could let yours set in the passenger area and have your crew member disconnect it and take it to the chase vehicle before you leave.