If the electric fan is "coming on constantly" I would really check your fan clutch. The mechanical fan is more likely to fail them the electric one. The auxiliary fan as I said before is ony supposed to come on when the car detects the temperature is getting too high as the mechanical fan isn't able to provide enough cooling.
I may live in Canada but we can get 40 degree (Celcius) summers too and the only times my car has "overheated" was when the water pump died, and when the fan clutch died. If you can stop the spinning fan with a newspaper then it needs to be replaced.