Heat conduction through an interface between materials may be considered anomalous if it tends not to follow the Fourier law. In the case of nanoscale heat conduction, this can result from scattering at interfaces and transient ballistic transport of energy. In this paper, we present a parametric model of anomalous heat transfer at an interface, providing a minimal parameterization for encoding of multiscale processes associated with this type of conduction. This parameterization is expressed formally in terms of effective thermal transport properties. Specifically, effective thermal diffusivities and interface-contact resistances, which adopted as physically-motivated phenomenological parameters, represent combined influences of underlying multiscale processes. The parametric model is demonstrated by simulation of heat conduction at an interface between a heated material layer on a substrate at a given ambient temperature, and inverse thermal analysis of a cooling inclusion within a background matrix.