Thermally isolated lateral heterogeneity in the earth's mantle has been studied in terms of idealized two-dimensional, constant viscosity, numerical models of mantle convection. Steady model solutions of the temperature and velocity fields were analyzed with respect to both the spatial and spectral signatures of their inherent lateral heterogeneity. By examining the changes in spectral signature produced by varying the Rayleigh number, the degree of internal heating, and the depth in the convection cell, it has been possible to identify whose features of the spectra of lateral heterogeneity which are most indicative of these variations. Particular attention has been paid to the spectral characteristics of thermal boundary layers within the convecting layer. The spectral analysis of known temperature fields represents the forward problem corresponding to the inverse problem of inferring the thermal structure of the mantle from the spectral components of its lateral heterogeneity as determined by seismic tomography. The forward problem presented here illustrates a new approach in convection modeling which may ultimately provide important diagnostic criteria for the interpretation of recent tomographic data.