I can't find a link and I think most places that work with thermocouples use a computerized spot welder now.
Maybe a little better explanation would work (I'll use a dual alloy thermocouple as an example).
The Carbon pot:
We used a 1.5 inch threaded pipe cap, just because

Drilled and tapped a hole in the bottom to attach to a piece of plywood and another hole in the side to attach a binding post. We had a 2 pound tin can of carbon powder that must have been surplus from Edison's lab. Fill the pipe cap with the carbon powder.
At this point you have a pipe cap bolted to a piece of plywood with a terminal to attach something electrical to it.
Needless to say it looks ominous and home made
To weld a thermocouple, make a twist at the end of the two different alloy wires so they will remain close together while welding. Use an insulated alligator clip to attach another lead to both wires. The purpose is to conduct current through both leads at the same time in parallel from where the clip is attached to the twisted end. When dipped into the carbon powder they will conduct, heat up and resistance weld at the point the current goes from the wire to the hot carbon.
We used a variac set to about 20 volts (just enough voltage for an arc in the carbon powder) for 28ga wires, but it would vary a little from alloy to alloy.
Welding: Wear goggles (not googles)
dip the twisted end (a single twist) of the thermocouple into the carbon powder, below the surface and keep it moving to keep fresh carbon next to the wires as they heat up. The glowing carbon will combine with any Oxygen in the air that is near the wires. Don't bump the sides of the pipe cap or you just welded the wires to the cap.
AC Current Flow: From one lead of the variac to the alligator clip, down the thermocouple wires to the end dipped in the carbon powder, through the carbon powder to the pipe cap, and back to the variac. Typically only tool about 3 seconds to make a nice little welded blob.
For a small ga wire to a larger gage wire, like a 28 ga Constantine wire to a 20 ga copper wire, make a single wrap of the smaller wire near the end of the larger wire, with a small amount of the larger wire projecting out. The weld will start heating the larger wire first then consume the wrap.
The one I made for home use had the pipe cap bolted inside a metal 3X5 card holder, with a flip top lid. I could store the leads and clips in the box. Just can't find it now. If I run across it, I'll post a pic.