If the coolant temp sensor is faulty, it will not signal to the engine that it has warmed up, and keep the mixtures constantly rich throughout operation instead of at the time of a cold start.
How long does it take for the cold engine warning light (no temp guage in city) to go out each morning?
Check the exhaust for carbon deposits since it should be clear and brown in color (engine runs on lean mode in normal driving). If it is black, then you have a rich mixture.
You will have to go through all that the others mentioned to check for what is faulty. Most OBD II scanners can give you realtime readings from sensors so you can run the engine and monitor coolant temp, rpm, air-fuel ratio etc at the workshop.