What on earth were they thinking feeding the regulators with 31V?
They wanted +/- 15 V for the analog circuitry. So they put 2x 18 Vac PCB transformers to leave some headroom for rectifiers, voltage regulators and mains voltage variation. With light load the transformers output 2x 22 V. Later mains voltage increased from 220 to 230 V and there you are. Since there was no space to have another set of transformers, they just took the same 31 Vdc for the 5V regulators for logic (DACs, shift registers and opto isolators). Instead of LM7805 they used LM340T-5.0 with a datasheet upper limit of 35 V. Now consider another +20 % mains voltage margin.
I solved the heat problem by inserting those very small Polulu switchers as down-converters to 8.5 V. The instrument also got a simple mains pre-regulator that dumps most of the excess power into two mosfets mounted on the enclosure frame, and instead of 31 V there is a constant +/- 22 V for the +/- 15 V regulators.
I also added schottky diodes over all +/- 15 V and +5 V supplies. Without such diodes JFET opamps may get killed after turning off power.
Something similar happened, when i looked into the HP3456A in-guard power supply. Building a good power supply with integrated voltage regulators may appear simple, but it needs some care.
Regards, Dieter