First, make sure you do not have 20A breakers on 14 guage wire. If you
do, change them to 15A breakers now. Thats what could be causing your
conduit to get hot.
Second, you should only have a double pole breaker for 220V circuits.
Although technically it will still work for seperate 110V circuits,
it's not proper practice.
Also you might have an Edison circuit, that is 2 circuits sharing 1
neutral, so its possible that even though you shut off 1 or 2 breakers
to a circuit, the neutral is still being used for your live circuit.
So the space heater you were using upstairs could be using the same
neutral for the circuits that you shut off. You need find out how your
lines were run, particularly in that junction box.