Not long ago I added a Mypin PID, same kind Frozone and others use. In 650deg lead it reads about 40deg higher than 2 reference thermometers. Fortunately you can program in a 'correction factor' and I've done that, but it still bugs me.
I know a bit about thermocouples and that they need a reference point of 32deg. Modern electronics fakes out this reference by taking the ambient temp and adjusting the TC output.
My TC plugs into a mating socket on my controller box and I used TC wire, observing polarity, to hook up the socket to the PID.
Anybody run into anything like this?