In case of diodes the powering and the sensing occurs on the same poles. Heating-up gives a larger error due to the power change during measurement as described above. Cooling and heating is symmetric, so you can always use cooling for characterization.
In case of cooling-down only a sensing current flows through the diode at measurement time, the simple case of separate sensors above can be used.
If you still want to measure heating up, the process for high-backlash three-pole devices above can be used, of course without the references to the voltage on the third pole.