Thermal Shutdown
I’m at Dell Headquarters in Austin, Texas and I just came across this thread. It sounds like overheating but to be sure see how long it lasts in hot vs. cold environments. Also you may be able to get more dirt out and get a better idea of whether or not the fans are in good working order by disassembling it and removing them. If you'd like I can look up the details of your system and possibly come up with more if you PM the details of the system.
Neil
Dell, Inc.