The flow of a thermoviscous body at elevated temperature under gravity is described by the mass, momentum, and energy balances of an incompressible, homogeneous, heat conducting, nonlinearly viscous fluid, in which the shear response includes a strongly temperature‐dependent rate factor. A scale analysis and coordinate stretching, appropriate for flows down an inclined surface, reflect the properties that depth‐to‐length ratios are different in both the “downhill” direction and perpendicular to it and that the flow is essentially from higher altitudes to lower ones. The normalized energy equation shows that, for the applications considered, in‐plane and out‐of plane (transverse) advections are important and that transverse diffusion and dissipation are both significant. Analogously, the stress‐deviator‐stretching relationship exhibits a conspicuous temperature dependence. Hence, there is strong ther-momechanical coupling.