This was passed to me by someone who is an expert in diesel exhaust systems....
For the OP ......tell him to look on eBay for "10M-Silver-Tone-Metal-K-Type-Thermocouple-Extension-Wire-TS and to use proper type K male and female connectors. It is also OK to use uninsulated crimp connectors to join the TC wires but cover them with heatshrink.
This expert makes his own thermocouples and extensions all the time. ...he says give him my email if he wants instructions on how to do the job cheaply and effectively.
So OP, if you need help, just ask me in a PM and I can hook you two up.