High Rpms and radiatorfan running at idle

[Major4eto]

Hello. I want to start this by saying im pretty new to cars and thats why i would like your opinion on this. I Have an Audi a3 2010 1.4tfsi. I Started having this problem with high idle engine racing at a red light. It was happening once in a while so i didnt really think much of it. i thought it was normal. But as time went on it started happening almost everyday. I didnt know at the time what was the cause for this but after a while i realised that the radiator fan was running and pushing the rpms above 1k. I went to a mechanic and got pretty much ripped off since i dont know anything about electronics and he said i had a non compatible battery and it couldnt communicate with the car computer and it was sending power there randomly. it sounded pretty believable so i paid 300$ just for a car battery since it was a “special programable battery”. At least the problem was away for a month or 2 and i thought okay i guess he was right since it fixed it. But a week ago it started happening again and its driving me crazy. He said the radiator fan should only come on for about 30 40seconds and turn off when the engine gets too hot. But mine does that on a cold start, when im parking my car, on a red light, sometimes on a optimal operating temperature, sometimes even in the first 2 mins of driving my car. Now i’ve heard that sounds like a DPF regen or something but since this is not a diesel its not normal. From what i’ve read a couple of people have said the coolant temeprature sensor might be the case but i dont have a check engine light. Would love to hear your thoughts.