I find that dialing *#*#4636#*#* leads to the battery temperature, but how does one discover the CPU temp.? The CPU is the greatest source of heat in the unit, and it would be good to have a number for that.
Twice this past weekend the phone shut down with a nearly-full battery and wouldn't restart to a working level until I took active steps to cool it, so I'm assuming these were heat-related shutdowns. Running apps included navigation and online radio while the unit was charging on the car seat in the sun.