Inside the TC08 data logger is a temperature sensor which is responsible for temperature compensation. It is sometimes refered to as cold junction compensation.
I suspect from your comments that the fan from the computer could be heating the TC08 unit and in turn mean that the temperature of the 'cold junction' has not actually stabilised. Also one of the rules for using thermocouples says that 'the temperature of BOTH the junctions (the connectors two pins) must be the same' and you are implying that they are not. Under these conditions you will end up with all sorts of errors as the connections become....... thermocouples measuring thier own temperature. I have never let it happen because it's so important.
Alternatively of course you could also have a really nasty P.C. which is giving out some really horrible electromagnetic interference. Or have a mains cable too close.
The best advice at this point is; be very methodical, change one thing at once and carefully observe the effect.
Such is the fun one encounters as an instrumentation engineer.....
P.S. if ANYONE else has any ideas don't be shy, let us know...