There is a new thermostat that is working normally when you remove it, the hose from the left side of the radiator (one that goes to the thermostat) is cold. The hoses on the right are hot. Left and right are from standing in front of car and looking at engine. Can it be my heater core or is it the radiator?

Check for possible corrosion or phosphate scale build-up, which may be plugging radiator passages. The radiator may need replacing. Afterwards, refill with a 50/50 mixture of VW-recommended antifreeze and distilled water:

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