Do you know what engine is in the car? That would be very useful information.
The coolant temperature sensor is a common culprit for cold start problems. There could be other causes. If you can find someone who has a VCDS interface cable and a laptop with VCDS software ([http://www.ross-tech.com|Ross-Tech]), you can look into what's going on with the engine and make a more accurate diagnosis. It's better than buying and replacing parts based on guesswork.