With just standard 4 mm connectors it is hard to use thermo-couples.
Some thoughts on the temperature measurement subject.
I think Kleinstein addresses a problem with the thermocouple solution, every junction with different metals participates in the measurement. And if those can't be tightly controlled then accuracy will probably suffer (but how much? Especially when the non measurement junctions are kept the same between pos and neg).
So RTD's seem a better choice if they cover the range one wants to measure. But when doing "live" thermal probing, without a solid thermal connection between probe and DUT, accuracy will suffer a lot from environmental cooling of the probe.
The bottomline is that great accuracies are almost impossible to reach, without "specialized" setups.
In this prove of concept:
determining-heat-dissipation-of-3d-printed-box-is-it-any-good I experimented in turning things around, instead of measuring different temperatures it measured how much power an enclosure can handle to keep a certain fixed temp. But that is a pretty time consuming way of getting information about thermal behavior.
So for doing quick and dirty measurements and doing reasonable accurate measurements a thermocouple seem to me the best candidate. However my hand MM has CJC, so its ready to use in that case. On the other hand there's no way of doing automated testing with it. (But that's would not be quick and dirty any more).
To conclude: creating a cold junction reference temp at 40 deg C, would (because of the handheld MM) mostly be a fun project, not one with huge benefits.