Details: The shutdowns occur at random times and are usually preceded by a scrolling gray semi-transparent screen and an alert that the computer is shutting down (courteous at least).
Sometimes if I try to power up immediately afterwards, I have to wait .5 - 2 minutes (is it overheating?). The most recent crash caused my email accounts to be deleted. As mentioned, the computer is out of service call warranty. I do have a Time Machine backup. Software is up to date.
I see in the forum that there might be both a software and hardware component to the shutdowns. I also see that full restore and special partial restores might fix the email problem (but am nervous about the partial since tinkering with Macs still feels like voodoo at this point). And I'd rather not spend $50 on a service call unless needed.
From the Apple perspective, what should I do?