So typically, you don't run thermocouples (TC) any longer than you have to because the wire is expensive.
You run the TC to a junction, if this is not the measuring instrument then the junction needs to be made using special alloy links that match the TC so that you don't introduce a larger offset in voltage.
From there you run special lead wire, this is similar to TC wire but lower precision.
Where it terminates at your instrument the device will measure those junction temperatures and apply the correct cold junction corrections.
Each step needs to be done correctly or you can get huge errors.
The TC itself is usually made by welding the TC wire, either electrical spot welding or torch welding (usually oxygen/hydrogen so that no C can be introduced).
When we were making our own TCs I would weld up 5 or 6 if I needed 3. Then bundle them in a heat sink block and put them in the lab furnace. I would record the readings (in mV) at various temperatures. If one TC was too high or low on readings, I would mark it and then destroy it. But I would have a set that matched fairly well, and a spare.
If they were for process control or certification I would send them out to a real lab for calibration data.
For example the Pt TCs in our heat treat furnaces all had serial numbers and periodic re-calibration.
It also matters what TC alloys you use. Today there is no reason to ever use "K", the drift on it can be awful. Use "N" instead.
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P.E. Metallurgy, consulting work welcomed
allows for on-site calibration, so we do ice bath cals if needed.