Hi there, Welcome! So, first off unfortunately I think I'm going to 'call' on the garage and say they didn't check properly. The thermostat is down the back of the engine about half-way down the block and VERY difficult to get to on 2005/2006 era, so them checking it and seeing it was new I'm a little dubious of. Anyway, did they run a coolant system pressure check, check the water pump output pressure or just check for no leaks? To me it sounds like a blockage, and typically that's the radiator on these as over the years they get blocked/partially blocked and don't do their job, slow down coolant flow, etc. Like you say, the filler cap being cool is suspicious, so where/how did it dump it's coolant? If it didn't foam out of the fillter cap it's gone somewhere, which makes me worry did it dump it in the cylinders (i.e. it's overheated too far and the head gasket has gone). First (easy) job for you at home is full coolant flush, get it flushed through the hoses and see how you get on. Then I think I'd go for a compression test to see if the head gasket is the problem. Thermostat could be stuck closed or almost closed but that's fairly unlikely, they tend to fail fully open. Good luck and let us know what you check, and ask the garage you took it to, what exactly did they do to verify the pump was working, etc. Did they pressure test the coolant system?