Decreasing dimensions of integrated circuit devices is leading to increased importance of microscale heat transfer effects and the failure of Fourier’s law in predicting sub-micron heat conduction. In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller than the phonon mean free path in the medium. Under these conditions, the phonon Boltzmann equation (BTE) needs to be solved in order to resolve the non-local thermal conduction phenomena. In this paper, the problem of an unsteady heat source of size comparable to or smaller than the phonon mean free path is considered. The unsteady 2-D phonon Boltzmann transport equation in the relaxation time approximation is solved using a finite volume method. The interaction of the heat-up time constant with the phonon residence time in the hotspot and also its interaction with the time scales associated with scattering processes are studied. The results are useful in assessing the peak temperatures during unsteady operation in microelectronic devices.