Heat flow and radioactive heat production data were obtained in the Canadian Shield in order to estimate the crustal heat production and the mantle heat flow. Several methods have been used to determine radioactive heat production in the crust. The analysis yields values for the mantle heat flow in the craton that are consistently between 7 and 15 mW m-2. Assuming that the lithosphere is in thermal equilibrium, we investigate the conditions for small-scale convection to supply the required heat flux through its base. For a given creep law, the thickness of the lithosphere, the temperature at the base of the lithosphere, and the effective viscosity of the mantle are determined from the value of the mantle heat flow beneath the shield. The viscosity of the mantle depends on the creep mechanism and on the fluid content. Wet diffusion creep implies a viscosity between 1020 and 1021 Pa s, corresponding to a mantle temperature of 1620 K at a depth of 250 km. The other creep mechanisms can be ruled out because they imply values for viscosity and temperature inconsistent with geophysical data. For a given creep law, there is a minimum mantle temperature below which equilibrium cannot be reached. For wet diffusion creep, this minimum mantle temperature (1780 K at 280 km depth) is close to that of the well-mixed (isentropic) oceanic mantle at the same depth. For a thermally stable lithosphere, our model requires the mantle heat flow to be at least 13 mW m-2 and the compositional lithosphere to be less than 240 km. ¿ 1998 American Geophysical Union