325 emissions fail

[swansea v6]

Booked in my 325 coupe today for a pre MOT check. It failed due to excessively high co values. Could this be linked to the fact I think my thermostat is knackered (stay with my technical terms here...) im thinking that because the engine doesnt really warm up, unless its been idling for an eternity, then the ecu thinks the engine is cold so overfuells, causing the high emissions????? does this sound reasonable or should I bite the bullet and give BMW my wage packet to take a look???? cheers........