Most tubes are fragile when they are hot. It is good advice to get the head off stage last.
When I was in High School, my band got kicked out of this house we were playing in.
It was about 10 degrees.
I had an old Sunn head, 100 watts.
We had been playing for a few hours, the amp had been cranked.
It never worked again after that night. The cold cracked all of the tubes, and I was too poor to buy new ones. The idiot at the repair place said the Output Transformer was dead and wanted $250. I was bummed.
I've only played in Hawaii for the last 7 years, so temperature wasn't a factor, but humidity was.
Tubes are as tempramental as a woman, but, once you learn how to not piss them off, they will treat you right.
Is there any way that you can let the amp cool at least a little bit before moving it or putting it in your case. It may be that the case keeps them hotter for a longer period of time and they are getting tossed around.