When done properly ( :x ) thermocouple extension wire (the wire that runs from the junction to the monitoring device) is made of the same material as the probe (the junction). (Some very misguided people will run copper or whatever from the probe to the meter, which is so wrong). Anyway, if you get some "thermocouple extension wire", strip insulation off the end, and twist the wires together, viola, it's a thermocouple. Ideally it would be welded, but if this is for a home project, it's good enough. I've done this with type J and type K thermocouple wire. I don't know if you live in the states, but if you do you may be able to go to your local HVAC supplier and ask them nicely for a few feet of the stuff. They may have type T, which is more common for HVAC. Then the trick is just getting something to measure the temp, as the junction will only put out millivolts, which is not linear, and I don't even think it's monotonic. Have you thought about a thermistor, instead? Much easier if you're doing roll-your-own temperature measurements, especially at low temps.
j.