2004 Audi A4 Car won't warm up

I bought my audi while living in florida. When there a CEL threw on my car of P2181 which was engine cooling performance. I returned to the original dealer and they replaced the ECT sensor and the code threw again two days later. Back to the dealer and they supposedly ran a full diagnosis and told me it was a defect in Audis and that as long as my car wasn't overheating that the code was fine. I didn't have the money to take it into a mechanic so I let it slide and kept a close eye on coolant and tempeture. I just moved back to Ohio and now am regretting not making the original dealer fix the issue. It just turned cold and now my car won't warm up at all therefore the air coming from my vents won't warm up. I noticed that my fan comes on as soon as I start the car and never shuts off.

My question is where do I start? The code is still a P2181 so do I replace the thermostat, the ECT sensor, or is it something else all together? I don't have the money to guess and it not be right. So I'd like to see if someone has a pretty definitive idea of what is wrong.