Hi welcome to the forum. Lots of useful information and helpful people.
Obvious problems could be blocked heater core, stuck/broken flap motor which directs the air over the heater core.
Put the heat on full blast, and check in the engine bay if the coolant pipes going through the fire wall are both hot. If not, then likely problem with either valve or heater core.
If hot water is going to the heater core, then it may be the flap valve motor, in which case, a VAGcom may have codes in the HVAC module. I'm assuming your airconditioning works?
BTW, not sure how you got 24 valves on your engine...Most of us have 20 on a 1.8T