In the research I did for my Master's degree in 2006-2007 I used thermocouples a lot for making temperature measurements. This was the first time I had worked with thermocouples. These are some lessons I learned about working with thermocouples, which may be helpful to anyone else in a similar position.
The best way to make a thermocouple junction is to weld the two wires together and there are machines made for this purpose. If you don't happen to have access to such a machine, it's easy enough to rig something up to do the job. A well-equipped electronics junk drawer should have all the necessary parts. The basic idea is to strip the ends of the wires and twist them together where you want to make the junction, then discharge a capacitor through the wires. The current pulse causes the ends of the wires to melt and when the metal resolidifies it forms a small sphere at the ends of the wires.
The wires I worked with had high enough electrical resistance (both because the wire was thin and because it was made of metals with poor conductivity), so it was necessary to make the electrical connection to the wires pretty close to the end where I was trying to make the weld. This is the solution I came up with:
The insulation was stripped from the thermocouple wires just far enough back so that the paperclip could contact the bare wires. The alligator clip helps hold the thermocouple wire in place and also makes the electrical connection to the paperclip. (The clip is the end of a patch cable; the other end is connected to a capacitor.) The ends of the thermocouple wires were twisted together for one full rotation and any extra wire past the first twist was cut off. To make the weld I simply grabbed the paperclip with insulated pliers and touched the ends of the thermocouple wires to a contact connected to the other side of the capacitor. The head of a screw works fine as a contact. The result is shown at right.
And that's it. The only trick is finding the right capacitance and voltage to use. For our thermocouple wires (AWG 36, type E) I found that 1160 microfarads charged to 50-55 volts worked quite well. (I got this capacitance by connecting a 1000uF capacitor in parallel with the flash unit from a disposable camera, which itself had a 160uF cap.) If the voltage is too low the wires will melt insufficiently or not at all. They may also end up welded to the contact. If the voltage is too high the tips of the wires just seem to be disintegrated.
And as always, working with equipment that can produce high voltage is dangerous. The above is merely a summary of the technique I used; I have not attempted to identify all the hazards present. Don't attempt to do something like this unless you can identify the hazards and proceed safely. You're responsible for your own well-being.