A shot in the dark at the spontaneous reset issue, but no clue on the 32 vs 64-bit observation...
See if ACPI exports any temperature readings under /proc/acpi/thermal_zone/*/temperature
and if so, keep an eye on them to see if there is an indication of a thermal problem.
( And if ACPI doesn't, maybe lmsensors can find something.)
cheers,
-Len
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