I have a 400P and have filled 8 tires back to back (33 and 35") from 15 to 30psi and never had an issue and takes about a minute for it to cool down. I would have not problem putting it back in the bag immediately as it does not get hot enough to do anything to the bag. I use mine all the time as I air down whenever I go off road. I have had it 2 years and it has never failed me. I think some people don't leave their vehicles running when airing up and it makes a big difference on how fast they pump up with the vehicle running when connected directly to the battery.

 

You should check out the viair 88p its rated up to 33 " tires and is less expensive has been working great for me

 

I have the 450P but I honestly cannot tell you the difference between the two. They are both excellent portable compressors. I use mine around the garage and keep it in my Jeep most of the time. Heat has never been an issue.

 

I have a Viair 400 with a pressure switch and 3 gal pancake air tank mounted in my 98 XJ which I have used around ten years for airing up 32, 33 and 35" tires. It takes a couple minutes to go from 13-32 psi, but I am pleased with its performance. Yes it does get warm, but cools off quickly when left into open air.

 

One of the differences you'll find is amps they draw. I got the 450P because it draws fewer amps which means less draw from the vehicle and cooler running. I've been very impressed how fast it fills my 33's.