We have studied steady convection with adiabatic and viscous heating for variable viscosity in the Boussinesq limit using the mean‐field theory. A strong nonlinear coupling is found between the thermodynamic constants governing adiabatic heating and the rheological parameters. We have established the range of rheological values for which adiabaticity would occur throughout the mantle. Too large an activation volume, greater than 6 cm³/mol for the cases examined here, would produce unreasonably high temperature at the bottom of the mantle (>6000 K) and superadiabatic gradients, especially in the lower mantle. Radiogenic heating plays a profound role in controlling dynamically mantle temperatures. Present values for the averaged mantle heat production would yield objectionably high temperatures in the lower mantle.