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The problem you have is a air lock in the heater matrix.
You can do the job yourself is you feel confident, make sure the coolant is cold, at the rear of the engine there are two pipes going into the middle of the bulkhead, undo one of the hose clips and loosen the rubber hose, start the engine and with the expansion tank top off, remove the rubber hose just enough to allow air to come out, once the coolant starts to flow refit the hose and tighten the clip.
Run the engine up to temp and recheck the heater is hot.
If it still blows cold repeat the step again, if that does not work then you need to have the cooling system check to see if the head gasket as blown.
Head gaskets are very common on this engine
2003 Jetta left rear window blue plastic part of the