Recent experiments on the melting temperatures of perovskite have indicated a high melting temperature in the lower mantle. This suggests that a creep law with an activation enthalpy, that increases strongly with depth, should be employed for the lower mantle rheology. We have examined the dynamical consequences of employing an Arrhenius type of dependence in a Newtonian flow law under the Weertman assumption relating activation enthalpy to the variation of the melting temperature with pressure. We have employed finite element techniques to model both steady state and time‐dependent flows for such type of rheology in an axisymmetric spherical‐ shell model. An outstanding dynamical feature from these models is the presence of a local viscosity maximum with a magnitude of around 10²³Pa · s for Earthlike surface Nusselt numbers between 10 and 15. This viscosity maximum is found in the middle of the lower mantle and is a site of high deviatoric stresses between 10 and 100 MPa. For the surface Rayleigh numbers examined (10⁴ to 10⁵) the flows developed are not strongly time‐dependent and often tend to a steady state. In spite of the presence of internal heating with chondritic strength, a few large, relatively stationary plumes are found in the lower mantle, while the rest of the lower mantle circulation is being driven by the more vigorous upper mantle flow. There are no small‐scale instabilities developed in the D” layer of these models, thus suggesting that any small‐scale lateral heterogeneities existing there may have chemical origins.