My ea81 has an aftermarket fan that is probably a little smaller than it needs to be as the needle climbs a bit when stopped idling in summer traffic, or creeping around on trails. I am going to install a larger one and if that doesn’t work I might try an oil cooler which should help or at least add a little oil capacity.
Sounds like you have another issue. EA71s have more than enough radiator capacity and normally never have overheating problems.
If your timing is too retarded it will cause overheating. Too much advance only makes problems when it starts detonating.
The fans only come in to play when you are stopped or moving very slowly.
Try gunning it with the radiator cap off and see what happens