Are your TCs floating or grounded? Basically, if your TCs are mounted to a metal test article and the object is grounded to earth, then, the TCs are grounded -- and very likely contaminated with ground loops. You will need to reference the TC inputs accordingly. These ground loops will cause the TC data readings to float - recall that TC readings are in the millivolt level. It does not take much of a ground loop to ruin a TC measurement.
Also, try this... first, set the filter to 10KHz and sample for a few seconds at 20 KHz (take 32768 data points). Now subtract the mean value from the trace and perform an FFT on the data. Look for the dominant frequency. Is it 60 Hz or some multiple? If yes, the likely cause is a ground reference problem.