I have a manual that says thermocouple extension wire doesn't have to be the thermocouple wire. But the joints between the extension wire and thermocouple wire must all be at the measured temperature.
Yes, to a point that is true but produces many problems. Here is the caveat:
extension wire and thermocouple wire must all be at the measured temperature.
Attached are a few images to help explain this.
The first is an example of CJC (Cold Junction Compensation) and the second is a typical Type K thermocouple. The thermocouple happens to be a dual thermocouple so ignore the additional two pins. With the thermocouple is a female thermocouple connector designed for type K thermocouple. The alloys in a type K happen to be chromel (positive) with respect to alumel (negative). The pins extending from the thermocouple are those alloys also, as well as the sockets in the connector.
At the tip of the thermocouple is the junction of those alloys and that junction produces a small voltage. At 0 degrees C that voltage is 0.000 mV and at 200 degrees C that voltage is 8.138 mV. So if I poke my thermocouple through the wall of an oven the hot junction (the thermocouple tip) will generate 8.138 mV. I can look at a standard Monograph Chart and it will tell me if I have 8.138 mV that the hot junction is 200 C.
Enter a problem as if I connect any alloy like copper wires to my connector I have created another junction of dissimilar alloys. Let's say that the ambient temperature outside the oven where I connect my copper leads is about 21 degrees C. Looking at my Monograph Chart I see that this new junction creates .838 mV. Unless my room temperature is 0 degrees C I now have 8.138 mV plus my cold junction of .838 mV and they are additive. I now have 8.138 + 0.838 = 8.976 which is about 221 degrees C. Note the small image where we see the need to subtract the cold junction temperature from the hot junction temperature. This is why it is a good practice to use thermocouple extension wire from the hot junction to the measuring device.
Would it matter? Truthfully likely not much because if I use copper wire from the T/C to my measuring device and the temperature at the input terminals of that device are the same temperature of where I connected to the T/C the device should apply a CJC offset and read relatively accurate. However, I don't see it as a good practice and it is a way to introduce errors into a measurement plane. Thus I suggested to the original poster to use T/C extension wire even though they stated the distance was short.
Just My Take
Ron