Hi
IMO it is a problem of lacks of contact somewhere.
When the system is warm, contacts usually are dilated and the contact become OK . . . now the problem is, where?
Is it a plain A1200 without an accelerator?
Have you checked:
socketed Kickstart ROMs
system oscillators (don't know if A1200 has socketed or not)
PSU plugs and so.
The worst thing, should be a cold/broken soldering that become conductive, when the mobo is warm.
Bye