Thanks, DJLA. This is a louder noise than the CPU, it lasted 5-7 minutes after I shut her down the other day, and it was coming from the rear of the engine. It was a hot day and instead of the fan continuing after shut-down for its typical 30 seconds or so, there was no fan, just this whine.
After reading Andy's post, I felt confident to drive it yesterday and was relieved to hear the engine fan running when I idled for a moment (it was a cool day, so it didn't come on while I was moving). The whine never occurred, which seems consistent with what I've now read in here about pressure relief valves and hot weather.
So now I'm hoping my fan has nothing to do with this, and will see what happens in a couple days when they're predicting hot weather again. If it whines, I'll remove my gas cap for the final test and will post here with the results along with the question of whether I need to replace the valve.
Thanks again for your input, you guys!