1. Since our gauges are not analog and since their input is a function of what the ECU tells them to say, there's a possibility that the truth isn't being told. This is somewhat mitigated by the fact that you replaced your thermostat.
2. Tepid air is likely coming from the electric element TDI's use to defrost windows before coolant temps come up.
3. Assuming that your engine is coming up to temp and since it isn't overheating, then it's fair to assume that your coolant is being heated and excess heat is being dissipated by the radiator. (This isn't always the case as diesels are efficient and don't shed a lot of excess heat.)
4. Cold lines to the heater core can then only mean that coolant isn't flowing into the heater core if warm coolant is actually in the system.
Bottom line here is that either the control valve is stuck or that your core or a hose is plugged. A simple way to determine if I'm correct is to bridge the coolant lines to the core at the engine and feel the hose after the engine comes up to temp. It should be hot.
For those as crude as myself I'd then take a clean length of hose and connect it to the input line of the heater core. You should be able to apply low air pressure (blow through the hose) and easily force coolant out the return line. This I'm guessing you won't be able to do. Which will lead you directly back to the control valve and the heater core.
Now there is one thing that concerns me greatly here. If you or someone who worked on your car has introduced the wrong coolant into the system, then I already know the problem without doing anything more than looking at your overflow container. Most often it's green coolant mixed with VW coolant and the two don't get along. You'll encounter a brownish jelly-like material as an indication of the reaction between the two.
If this be the problem, then it's time for a mandatory flush of the entire system with the hope that the jelly has yet to chemically combine with the internals of the engine, radiator, and heater core. Otherwise you'll be putting some expensive components on your shopping list and cursing whomever made the mistake.
Oh... Lewis Center, NY?
