We are told that particular thermocouple types can be expected to produce specific, measurable voltages which correlate in known fashions to temperature. That's fine, but actual results may vary when high precision is needed. A sometime overlooked contributor to measurement error is the temperature gradient along the length of each thermocouple wire.
This sketch shows the issue at hand.
If the thermocouple junction is really hot, shall we say 1000°C, you are not going to want to have your metering anywhere close by. The thermocouple wires will need to be of some length away depending on how far from that hot spot your metering devices need to be, let us say some number of feet.
Even though each wire is of the same alloy along its entire length, even though it is of the same chemical composition along its entire length, each incremental length will be at a slightly different temperature than its adjacent incremental lengths.
All of those adjacent incremental length junctions are themselves thermocouples which will then be making thermocouple voltages of their own, thermocouple voltages that are entirely apart from that of the intended thermocouple junction at the hot spot being measured. Also, since the two lengths of wire are of different metallurgical composition, the incremental voltage gradients along the two wires' lengths will be different.
This effect can be of concern for high accuracy situations. It is mentioned for example here
... where we find the sentence ... "This thermoelectric voltage is produced by the temperature gradient along the thermocouple wires. The thermoelectric voltage is not produced by the junctions themselves."
In your application, perhaps this won't matter. In many cases, your accuracy requirements won't be stringent enough for this to be important, but on the other hand, maybe it will matter in some cases.
At least remember to bear it in mind.