If I notice the temp gauge climbing on any of my equipment, I stop working it and keep the RPMs pretty high. Not WOT, but well above idle. The engine turns the fan and the water pump. Without circulating coolant, the great has nowhere to go. It the temp didn't start going down, I'd shut it down, but that's never happened. Once it goes down to where i want it, then I shut down and clean the radiator.
Next time, keep a closer eye on the temp gauge and don't wait until it's overheating. In some conditions, you may need to clean the radiator quite often.