I assume you have climate control, and if you set the temperature to be 21 degrees for example the hot/cold servo motor will move as required to maintain the interior temperature at 21 degrees. Now obviously when the engine is cold this temperature may not be reached, and the servo motor will probably be in the hot position until the engine warms up. It will move to a cooler position as the temperature increases, and 21 degrees approaches. Whether the A/C is on or off will not affect this at all. The heater will still be hot if it's demanding hot even if the A/C is on. The inside air will be conditioned and humidity will be reduced. If you set the system to 'HI' then the servo motor will stay in the hot position and the interior will be hot. Similarly if you set it to 'LO' it will stay in the cold position and the interior will be cool.

The most likely reason for your heater being cold is a failed water pump. Many have plastic impellers that break away from the steel shaft allowing them to spin freely. You may notice your engine temperature gauge increasing too. This is another sign. A new water pump and cambelt may be required.....