Fan stays on full speed when engine is on
 

Hello all of you mini cooper guys, I'm new in this forum and I need your knowledge and expertise please :).
I recently bought a 2004 mini cooper, I like it a lot, it's like a go-kart :).
My issue is that when I turn the engine on, the fan radiator straight away goes on, and stays like this until I turn the engine off. The fan goes full speed.

I've checked online, some people have this issue but when they turn off the engine off the fan still keep going, and they were talking about the fan relais. My issue is slightly different in the sense that when I turn the engine off, the fan goes off too.

Any idea where to look at first?
Also I'm leaving in Vancouver, Canada, just so you know, I don't think those cooper are different from the USA or even Europe, but I'm definitely not an expert.

Thank you guys for your time I really appreciate your help.