It can be much simpler than that. Maybe an I/O pin is left floating by accident (neither pulled up or down) and below a certain temperature, it gets toggled and brings the machine down. We actually had this exact problem, but it was the other way around: The floating pin was pulled the wrong way after a certain temperature was surpassed.
Not temperature, but I once had a tiny speck of solder bridge two address lines together on an EEPROM. Drove me nuts figuring out why my attempts to program it kept failing after installing a JTAG when everything else I read worked fine.