Why cooling fan turns on even at engine cold start? This started happen recently

What is your question?

My 2002 Mitsubishi Lancer's cooling fan turns on even in the morning when I turn on ignition key at cold start. This starts happen recently. Other than that, the fan operates normally when it suppose to. I replaced both the temperature switch and the cooling temperature sensor. But the problem still persist. I am not sure if this relates to cooling fan control module or the cooling fan relay, or I have to consider replacing them. Any advice would be highly appreciated. Thanks