iPhone - Running hot, odd CPU usage
I finally found the issue!

It was an iPhone game called Minesweeper which runs as a widget in the Notification Center/Today View. I guess to be in the Notification Center/Today View as a widget, it has to be running, yet it was not listed as a running app when I double tapped the home button.

I have no idea why Minseweeper was causing the high CPU or why it occurred randomly, but as soon as I deleted Minesweeper, the problem went away.

The only reason I discovered the cause of the problem was because I was in the Battery app in Settings and I happened to tap a section of the Battery Level graph and it showed app activity for that specific moment in time. Minesweeper was there at 30% usage and I hadn't run that game for months.

I hope this solution helps someone somewhere!