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Why does the electric fan keep on running, on some cars, after the engine is turned off?

I want to install such a system on my car and I dont know whether to wire it like this or so that, when the engine is turned off, electrical power to the fan is cut off as well..

The stock car is equiped with a fan on the water pump..Which will be removed.

The thermostat which i`m going to buy closes the circuit at 86Degrees C.