>> my thoughts go the following path: possible little spare margin of 
>> cooling power by original design -> aging -> [...
>
>This could be.  It hasn't been sitting idle for all that long, only a few
months, but you never know.

  it's not the time sitting idle, but the 'warm...hot life' before that
has the relevant impact on aging - shelf life (="time sitting idle") of
electronic components is close to excellent
  it's different for mechanical components such as bearings found in blower
fans:
by not being use they tend to become "sticky" -> less RPM -> less airflow 
-> less cooling power  (I _beleive_ "goo'ool" DEC workstation & server 
equipment was designed taking care of these facts...)

>
>> you also mention hot circuits near the connectors to the outside 
>> world, right?  may it be that the venerable machine suffered an a tad 
>> to strong dircharge (think surge, ESD or the like) ?
>
>I suppose it could have been, but I doubt it.  Some of the reasons:
>
>- The machine wasn't connected while it was sitting idle.
>
>- The external-interface electronics still work.
>
>- The heat is coming not from the daughterboard, where the interface
>  electronics that would take a hit are, but from the motherboard just
>  below it.
>
>- The two places that are running disturbingly hot are both populated
>  by the same kind of chips (small square surface-mount packages of
>  some 20 to 30 pins each).
>
>The power supply idea is a good point; I should find an accurate voltmeter
and measure the supply rails.
>

  the "accurate voltmeter" you are looking for is a scope! (oscilloscope)

  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"

good luck
Stephan