Intermitent AC, 04 Passat, blower works but no cold air

check it the heater control is allowing hot water through the heater core.(turning the tap on )

If you are talking about the belt for the ac compressor, yes the heater should still work.
If the blower is not working, you will need to have the blower motor checked for voltage and ground.

check the blower relay or have someone test the ohm resistance on the fan motors and or relays. also check all the fuses that deal with the heater and blower.

The blower motor resistor may be the cause of it not working. They cost roughly $12. Here is a video on how to replace them:

Vw passat b6 2006 -2015 heater blower fan resistor replacement ...

I would try to isolate the blower motor power connection, disconnecting anything from the motor and jumpering 12V DC directly into it to see if it will run when power is applied. That would rule out a bad motor. These are good places to start.

The A/C in my 2006 Passat 2.0 T is not working consistently. It seems to quit giving cold air when the outside temp is the hottest. It sometimes works fine until the engine is warmed up-then starts blowing hot air. Any Ideas?

First-check fuses.If O.K. remove blower motor.But before that check for power on a motor terminals.Sometimes the resistor make the same problems.Located into blower motor housing

Sounds like your ac needs to be recharged with fluids, not DIY job but should not be expensive at a drive in depot if you shop around.

good day, you may have some heating core issues, anti freeze leakage, have it checked. hope this helps, have a nice day

check antifreeze level also check the fuses to the blower motor