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).
Put a link wire across the two spades and see if it fires up, if it does then so long as the switch is OK, it will run....if the switch is not OK, why not just replace it so you don't have to worry about manual switches.
I'm out of the dark ages now - all the vehicles I drive can look after their own cooling without my help
The fan works, did jumped the connections the other day to check it.
Cleaned up the spades while they were off, and now I'm just waiting to run it up to temp to see if it works yet. If it doesn't, I'll probably just put a switch in, as I can't be bothered to replace the otter switch, too much hassle,
The car only ever goes over the normal mark on the very hottest of days regardless of what it's doing, so won't need the electric fan most of the time anyway.