Corolla Radiator Fan Problem

[Mark Usman]

Hey guys - I'm new to this forum and looking for some help. I own a Corolla 2013 Model, its radiator fan turns on and won't stop "sometimes"...other times it works normal as it should however once it goes in the "on at full speed all the time" it won't stop. I have figured out a way to put it to stop and that's to remove the 3 pin connector on the computer controlled fan module and plug it again and it would stop the fan immediately (provided there's no ac on and the engine is not too hot). I have replaced the fan module but that didn't help. Also, the temp sensor as well as the air conditioning works fine although I haven't turned the ac on in a while because of winters already. What could cause this 2 speed fan to go on at full blast and stop by unplugging and re-plugging the 3 pin connector on the fan module? I'm confused. 

Thanks so much!
Mark