Whew.....good going. I'm sure you will have fun with the hot tub.
To extend a thermocouple, you can buy small male/female mating connectors specifically designed for thermocouples. These come in different colors for the different types of T/C's- if I remember correctly (but don't hold me to it), yellow connectors are for type K's, and black ones are for type J's. The connectors, as well as the extension cable MUST be of the same type as the thermocouple. If different types of connectors or extension cables are used, then each connection point becomes its own thermocouple junction, adding or subtracting the voltage it generates to the voltage generated by the thermocouple, inducing large measurement errors! I've worked on industrial installations where thermocople runs in excess of 100 (and even 200+) feet caused no problems or reduction in accuracy.
The different types of thermocouples (K, J, T, etc) are made by using different metal combinations, and all have different temerature ranges and voltage/temperature curves.
Hi I totally agree with Sue and Gary about having to use the special cable or you will have problems I would also suggest using the special plugs and sockets mentioned earlier to prevent any "additional" thermocouples being formed due to disimilar metals being in contact even the terminal screws were of different metals so don't mix them up. If I remember correctly these plugs and sockets are also polarised but can not remember which colour goes to which terminal. It is over 15 years since I used thermocouples. so I can't be of any more help, sorry. Maybe one of the others can remember the plug polarity.
73 Nick G0CWA
Here is a source of thermocouple information and products.
Pull my finger. Part II. On second thought, pull your own finger.
You will be creating a junction when using different wires. Not a good way to go.