>> when DC power is/gets noisy/spiky/ripply this does not necessary mean
>> that the average voltage (the value all DC voltmeter show you) goes
>> "out of band"
>
>True enough.  But (a) it can't _hurt_ to check the average DC voltage,
>and (b) since everything works when kept cool I am inclined to doubt
>that noisy power is the root of the problem.

the noise on the power may be right on the edge of "still good"
an be tolerated by new chips at any (reasonable) temperature whereas
aged chips tolerate it only when cold, but no more after they have warmed
up...
(hey, ageing _does_ affect electronics!)

(how?) can you tell for sure that either:
 a) "heat is source of problem"
	the chips cant dissipate their heat as originally intended, 
	warm up too much and therefore behave erratically 
or
 b) "some problem causes/is source of the heat"
	something (e.g. too noisy power or a former ESDischarge, etc.) 
	really is the problem and brings the chips to warm up excessively

answering this should bring you closer to a solution

good luck
Stephan