If one uses the "classic" (HUUUGE) thermocouple connectors, these have a hole in the middle for a sensor.
But they are hard to use due to size.
Most equipment manufacturers use normal screw terminals. I know some glue a thermistor, or even a diode, to the back of the terminal block.
But let's say you are using a plug-in screw terminal. Then there is no way to measure the temp of the plug-in portion, which is likely to be a few degrees cooler than the sensor - even if the sensor is on the PCB and right next to the PCB part of the connector. Experimentally I see a delta of about 3C.
I reckon they must be compensating for the delta-T, and this is probably constant over the usual temp range because for a given power dissipation the delta will be constant over ambient, to a first order... One could also measure the incoming power :)
And thermocouples aren't usually expected to be super accurate...