I got some private messages from Dell Support asking me to troubleshoot the problem by running a program that continuously logs the temperature of the CPU cores. Unfortunately I don't think it will continue to run after the system goes to sleep, but I didn't have time to try. My workaround is to automatically turn off the screen after 10 min and never go to sleep. That has solved my problem (as long as I never forget and set it to automatically go to sleep in the future).
I've had my desktop all in one PC for about 3 weeks and this has happened several times. If I put the system to sleep and walk away everything is fine. If I walk away and it goes to sleep after 10 min (I think, I've never watched it long enough to say) and I come back some time later, it seems to have overheated and shut down. I can't even restart it with the power button, I have to unplug and replug it in before starting it up. Then the fan races and pushes out hot air for a few seconds as it starts up and then everything runs fine. I have a second one that I bought for my wife a couple of weeks later and I fear it might be starting to do the same thing. Is this a known problem? What can I do to troubleshoot it? 
Optiplex 7780 AIO Unexpectedly Shuts Down When Asleep