You can turn on most power supplies by shorting the black and green connectors near the center of the
mobo connector. You could run wires from those connectors through a switch located somewhere on your comp. Or you could run them to a solid state relay switch powered by your primary
PSU. When the comp is turned on...it supplies power to the relay...and the relay switches on power to the second
PSU.
I don't know if condensation would be a big problem. But a little dialectric grease on the processor pins and some neoprene foam around the processor and hoses wouldn't cost too terribly much for the peace of mind.