Temperature readings are not as easy as it may seem to be.
If you find a thermo-couple that can read temperatures more precise than +-1°C it is already a REALLY good one!
Is the thermocouple officially calibrated? (Normally you get some sort of certificate if it is calibrated...)
E.g.: Usual simple digital thermometers for the air temperature that cou can buy everywhere show some stuff like "23.2°C" and make the customer think: wow - it shows the temperature 0.1°C correct! - but that's just a marketing trick. These thermometers (at least when they are cheap) often vary up to 3 or 4°C!!! If you have a better one it will be +-1°C accurate and a really good (and really expensive) one maybe even less than that.
So if it is not calibrated (I think that you would need a calibrated thermocouple and tested, also calibrated software or an "build in" display) you can't say which temperature is wron. Maybe the CPU displays 1° less than the true temperature and the thermocouple about 1.5° more... mabe one is exact and the other one is far away...
I study physics and even with calibrated thermometers it can be very tricky to get a reliable and good temperature reading. You should also take care if the calibration has beed done for the temperature range you are interested in!