what is the real DC power dissipated by an inductor that is pulsed on off
It is very difficult to perform an exact caloric measurement of dissipated thermal power on an inductor. But I have to assume you did the necessary prerequisites.

Besides this there are some possibilites for errors.


Electromagnetical power can be radiated during switch on/off. The percentage depends on duty cycle, inductance, dimensions of coil and frequency of switching. However EM radiation should not show up in DC power if measured properly. But meters with poor quality will deliver tainted results.
If other metal parts are around you may induce eddy currents which maybe deliver the thermal power outside your caloric chamber. Depending on the ferromagnetic properties of those materials they may lead to (virtual) DC components in your measurements especially with odd duty cycles
If your inductor is soldered somewhere you may encounter the Peltier effect. So DC power is converted to thermic transport power (reduction of local enthropy) instead of thermal power.
The leads to your caloric chamber may dissipate substantial thermal power, not only by ohmic heating but also by thermal conduction.