I have mazda 6 2005 .. the problem is the cooling fans not shutting down when idle unless i step on gas.
Temperature is stable btw no over heat.
It used to come on for 15 sec maybe then shut down but now they are on all the time unless the car is moving or stepping on gas.

 

sounds like you need a new fan relay its near the fan and a square box. I had the same issue on my 04. They are cheap and easy to fix.