Collisions of Thermal Impedances
The graph you show (for short time durations) is governed by the specific heat capacity of the material in question. For longer/extended time periods it is governed by the thermal conductivity of the material. Specific heat capacity for most common materials (and possibly most uncommon materials) falls with temperature hence, at lower temperatures, a particular material will exhibit what your graph shows at short time durations.

If you want to find out more, examine the specific heat capacity for the material in the IGBT.

Do we have the aforementioned phenomenon in RC circuits

No, an RC model of the thermal properties of a material is not reflected in a change of capacitance - the model assumes that the thermal properties remain constant unless there is particular attention paid by the model designer to making capacitance change with local ambient temperature (I've never seen this done BTW).