kernel task at ca. 100%, fans not running, temperature sensor defect?

My MacBook Pro (early 2011) was working fine under Yosemite until 5 days ago. I then upgraded to Sierra, however, since then, every time I boot it, after a few minutes the CPU usage goes up to almost 100% and the Mac becomes unusable, even if no app is running at all.

Furthermore the fans are not working anymore, even if I start apps with heavy workloads my Mac doesn't become warm and the fans don't start running.

At the Apple store they diagnosed a defect temperature sensor, however they couldn't help me because my Mac is older than 5 years.

I would really appreciate any help, thank you!