Heat RElated Problems?

I am trying to solve a problem for a friend. This is an older computer. HP Pavillion 533W
Celeron Processor ~1992 Mhz (from sysinfo). 1 G Ram

She reports that her "computer keeps shutting itself off" but then "comes right back on".

I am thinking heat problems so I installed SpeedFan and got the following result

Fan1 Asus Mozart-2 Speed 2021 Sensor Temp1 Temp 35°
Fan2 Asus Mozart-2 Speed 0 Sensor Temp2 Temp 85°

The fan on the CPU is spinning freely but there are no other fans on the MB. I've touched every chip I can find and none seem to be hot.

My question is - Is there truly a Temp 2 Sensor that is monitoring something? If yes, what is it monitoring?

Could it be a bogus reading of 85° that is causing the the intermittent shutdowns.

Thanks,

Dave

Thanks for your comments -

It has been sitting here for about 12 hours with a couple of windows open but not doing any processing.
I can try only the BIOS but I suspect that having Windows running is more realistic.

I've asked her if there is a way to replicate the problem but haven't received a response.

PSU was replaced within the last month for a similar problem.

NO BSOD that I am aware of.