Dell e6220 cpu idle temperature high 65 degrees and fan running constantly

Since last week I noticed that the fan in the Dell e6220 is running almost constantly even while the the CPU usage is low (5-20%). The indicated temp is constantly around 65 degrees, which is too high for such low usage.

I'm unable to find out why this is happening, what I did:

- ran the Dell diagnostics at boot time, which doesn't show an error. However, it shows that pre-boot the CPU temp also gets up to and stays around 65 degrees, so the problem is not OS / usage related. I've let it sit for a while and when I flip my notebook, so the bottom side is also up in the air, it cools down a bit more to 51 degrees and the fan stops running for a very short time. The CPU temp shoots up again and the fan starts running again.
- the fan is working properly and is going up in steps to max when the CPU temp goes up
- I have never really checked how warm the hot air blown out actually is, but it seems to cool like it should
- checked for dust inside around the fan and openings, but everything is clean
- the heatpipe gets as warm as the heatsink, so the heat seems to be transported correctly (I thought that the heatpipe might not transport the heat anymore)
- the heatsink gets warm, but is clearly not that warm as I can touch and keep holding it, so I'd say it's only around 40 degrees.

Would it then be the thermal paste connecting the CPU to the heatsink that has dried out? Where is the actual temp measured? This may explain the difference between the heatsink temperature of about 40 degrees and the read temperature in the system of 65 degrees.

What else can I check to find out the cause of this problem? What else could be the cause of this problem?

Hope someone can help!