For anyone interested here are the first round of results:
11:40 Battery has been removed for 10 minutes. Baseline temps:
Battery: 80
Screen bottom: 82
Screen top: 81
11:42 Battery inserted powered on Screen works
Battery: 81
Screen Top: 82
Screen bottom:82
11:45 Still on screen works
Battery 85
Top 83
Bottom 87
11:48 Still on screen works
Battery: 89
Top: 84
Bottom: 91
11:56 Still on screen works
Battery: 94
Top: 87
Bottom: 96
11:59 Pressed power to put screen "asleep" then immediately tried to wake, got black screen, can still swipe to unlock.
Battery: 95
Top: 87
Bottom: 96
12:00 Pulled battery and immediatly replaced, turned on still black screen. Pulled battery
Battery: 95
Top: 87
Bottom: 95
12:04 Replaced battery, turned on, still black screen, pulled battery
Battery: 88
Top: 86
Bottom: 89
12:06 Replaced battery , turned on, still black screen, pulled battery
Battery: 86
Top: 85
Bottom: 88
12:08 Replaced battery, turned on, see HTC boot screen
Battery: 85
Top: 85
Bottom: 87
12:10 Fully booted and screen sleeps and wakes fine (note: data is 1x briefly)
Battery: 88
Top: 85
Bottom: 88
12:12 Put screen to sleep, try to wake, black screen
Battery: 90
Top: 85
Bottom: 90