Quite often there will be an internal temperature sensor such as an LM35 which is supposed to sense the temperature where the thermocouple wires solder onto the PCB or go into a screw terminal block (yet another junction).
The voltage across this unavoidable internal junction is compensated for by the LM35 either in hardware or sometimes in software.
It all works, provided everything except the actual probe tip is allowed to settle and fully assume correct ambient temperature.
But its also easy to screw things up if we start mixing different coloured plugs and sockets with different thermocouple types, or as Brian points out, connecting the right type of plug to the right thermocouple the wrong way around.
All the plugs I have seen are marked + and - so that at least is a guide you can probably rely on. But the colours are probably more of a trap than a help.
Its not easy, because there many companies supplying thermocouple wire with different colour coded wires, and as we now know, there are two standards for plug top colours. You absolutely must correctly identify the thermocouple wire and plug, and know where (which company) both came from originally.
If you get it right, thermocouples can be very reliable and surprisingly accurate.