I too would look at the CPU cooling issues first, may not be logs to see but the physical box is worth looking at.
I'd have the case apart and lift out any dust, re-seat the RAM, Video Card (if it has one) and pinch up the motherboard mounting screws, try it then if no change remove clean re-thermal paste and replace the CPU fan assembly.
Just because the room is cold the fan could still be running slow or full of dust.
Very long shot...
I had one Supermicro server motherboard that would seemingly random reboot until I found the mounting points had oxidised and the Mobo grounding was sensitive and bad, quick loosen and pinch up mountings got it stable again. I know that is a real long shot but someone has to benefit from the hours I spent tracking that down
