The control head has a systemic problem with these cars. If BOTH sides are dumping heat into the cabin when not asked for, I see a minimum of two potential issues here. One, the duovalves may not be adequately commanded to 'close', and the blend door may not be closing off the hot coils in the cabin. Turn both temp ***** to one detent from max cool, and feel the individual lines at the firewall. If the lines are hot as all gitgo, then the control head is not sending a full signal to the valves to close (after car is fully warmed up). I postulate the blend doors never do seal 100% so that may not be your issue. Full hot heater coils (drivers side and passenger side) will leak heat into the cabin even if the blend doors are working correctly. There is a fix offered to the control head, that involves taking it apart and 'reconnecting' intermittent pins on the PC boards (that either vibrate loose of build up oxidation on them until vibration reconnects it). This definitely explains the 'working now' but 'not working again' some time later. Check if the heater lines are extremely hot first, that might help narrow down if the control head is the problem.
Of course, you made sure the duovalves coils are not burned out, right? Unplug them and check the continuity with a simple ohm meter. After that, you can test if the head is sending a signal to them. You'll see a pulse (voltmeter jumping) according to the individual cabin dial settings. With both set to full cool, you should see each valves coil having constant power to them (might be a minor 'off' in a rhythmic pattern to keep the coolant moving). Remember, these valves are set up to failsafe in the flow (open) position. This means when the system has a problem in cold weather, you'll have heat through the coils.
Finally, you have to make sure you allow the car to fully cool down before you try to troubleshoot different things UNLESS you know things like if you disconnect the duovalves the flow will make the coils hot (no signal to close them). If you think having the car off while the system is hot (to check the coil continuity), you may find the temperature differences caused a thermal flow to occur causing the coils to be very hot and influencing your results.
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