I need to know roughly what the precision on a J or T type thermocouple is?

Question

I need the precision not the accuracy. Accuracy should be around 1 to 2 degrees C.

Answer 1

I think precision of your temperature measurement system would be virtually the same as that for the meter that is sensing the voltage and displaying the temperature.

Answer 2

The thermocouple is about that accuracy

But you are not measuring 40uV per deg C above the cold junction without the help of a thermocouple converter with a cold junction compensation

Added to that there a compensations leads which must be used to preserve accuracy

By far the biggest source of error is the converter
(which has to be calibrated anyway)

Answer 3

Precision depends purely on the measuring circuit and not on the thermocouple. Measurement of maximum or minimum temperature depends, of course, on the type of thermocouple.
I hope I understood your question well.