Fluke 51,52,52,54 Series II Thermometer Service Manual does not have schematics. I'd uploaded it to BAMA long ago but most of the batch did not get posted.
You'd have to take it apart and post pics to see what the CJ sensor is, assuming it is broken.
You could check the calibration, for both the cold-junction and A/D.
Reference Junction CAL:
Type K thermocouple in ice bath.
Enter CAL mode (poke the tiny CAL button hole on the backside), LCD shows one of 4 menus: CAL A-d, CAL rEF, CAL donE, CAL Abrt.
Select CAL rEF, press enter, arrow keys up/down until temperature matches known temperature, press enter, shows CAL donE, press enter to store.
Or up/down arrows to CAL Abrt, press enter, to abort cal changes.
Calibrating the A to D needs a precision voltage source where you can dial in +80.000mV and -8.0000mV
There's an offset feature too in SETUP you could see if it's zero.