In this study, explicit criteria are derived for the applicability of the uniform temperature approximation (UTA) to unsteady heat transfer through the solid phase in assemblies of spheres. The sources of unsteadiness studied are temperature, variation and contact area variation. It is shown that, for the case of temperature variation, the UTA cannot be used for a certain range of frequency of the fluctuations. For the case of contact area variation, the UTA is shown to be applicable in all cases, provided that the contact radius is smaller than 10% of the particle radius. Following the assessment of its validity, the UTA is employed to illustrate the effect of aggregate and deposit morphology on the aggregate thermal relaxation behavior, considering the limiting case of linear aggregates, and simple two-dimensional on-lattice deposits.