I'd suggest trying to find what the underlying problem is and fix that.
Pretty sure a standard mini should be able to cope with anything here in the UK, even the current heatwave, 
I think mine needs a flush as it did go just over the normal mark (needle thickness over) the other day, putting the heater on (just opening the tap) dropped it back down again (didn't get any hotter in the car as it was already too hot,
).
My car has the standard rover electric fan, but it's not been working since I've had the car, tried to get it working yesterday by cleaning up the contacts, just got to see if it makes any difference the next time I go out (or if it even works, might end up just having to mod it to a switch inside if the otter switch is broken).