[bb123]

I don’t think this is true - this is completely normal behaviour. The cooling fan is coming on due to a phenomenon called heat soak which is where the engine temperature increases above normal for a time after it has been switched off due to the lack of coolant flow. The fan is coming on to aid cooling the engine/engine bay to reduce the effect of heat soak.

With carburettor fed engines it is sometimes advised by the manufacturer to allow the engine to idle for some time after running it at high RPM. This is because the effect of heat soak can be significant enough to boil all the fuel off in the carb, making the engine hard to restart when hot.