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Please have a look at the attached cooling system diagram. The cabin heater always has coolant circulating even with the thermostat closed. If the problem was a bad thermostat you would have extreme heat output. So since you have no heat you either have no coolant circulating or your climate control system could be malfunctioning. The common denominator to your symptoms appears that you have an airlocked system or a water pump with no impeller or accessory belt is missing. You might check the belt is still there and if it is I still recommend you to purge the system. The tank can be full but will boil over when the engine overheats. If you can get an Airlift great otherwise Pedro has a procedure you can use on his DIY site.
Please also note there is no temp control valve to the heater. Heater always has full coolant flow. Increasing cabin heat simply redirects more heated air to the cabin.