How can I fix or change my engine stat?

Hi, I hope you can help me? I was wondering how easy it would be to change or fix a stat on the my engine? It is a 2003 BMW 325ci sport and the engine fan keeps on running even when the car is turned off and then eventually runs the battery flat, the only way I can stop it is to remove the fuse for the fan but then the window blowers don't work. I was told the stat may be jammed on? Is it a simple job to fix? Your info will be really appreciated.

Many thanks.
Adam