The governing equation for the temperature response of small particles subjected to diffusive and radiative heat transfer in a homogeneous medium is derived. The method used to derive this integro-differential equation is based on an extension of Duhamel's superposition theorem and it is simpler than the Laplace-transform method traditionally used. This approach is also used to discuss the origin of the history term, which is shown to be a Riemann-Liouville-Weyl half-derivative of the temperature potential between the free-stream and the particle surface. This observation is used to derive the scaling of the unsteady and the quasi-steady contributions for harmonic perturbations of the background temperature field. We identify a scaling number SR, which is a normalized dimensionless frequency, that measures the importance of the history term as compared to the quasisteady diffusion and radiation contributions. The relevance of the scaling analysis for turbulent flows is discussed.