I'm measuring the temperatures of my Q6600 with Coretemp.
I'm leaving this program open all the time when I use my computer. Is it possible that my temperature sensor of the cpu breaks because I am seeing it too much?
The temperature sensor is reporting data whether you are looking at it or not, core temp just makes that data readable by you. A temperature sensor can break just like anything else, but nothing you can do will cause it to break faster or slower.
If you're having extreme temperature fluctuations or the values are strange (-10*C on one core, for example), then you might have a broken sensor. Otherwise little exists that you could do to damage the sensor one way or the other.