heater shouldn't be affected by thermostat operation, other than if the 'stat has failed it'll either take longer to warm up (stuck open) or engine overheat (stuck shut).
i'd say there's air lock in the heater core. as you rev engine, coolant flow is higher so you get a bit of flow through the heater core but not enough to clear the air lock or produce heat when at idle.
I'm not sure if you can get to them easily on the 8gen,but have a feel of the pipes that go through the bulkhead to the heater unit and see if they get warm. They should go through behind the gearbox area. you'll then know where the heat is/isn't getting to. saves spending any money just yet.
you should have heat on both feed&return pipes, albeit return should be a bit cooler.
I would have thought if the Coolant level was really low that the car would be overheating? My Mrs Punto had similar symptoms.. Cabin temperature didn't get as hot as it should and when at Idle the temperature guage actually dropped.. I suppose checking coolant won't do any harm.