We have studied the consequences of including temperature-dependent viscosity in mantle convection with both of the major phase transitions included. We have employed a two-dimensional cartesian model in a box of aspect ratio four. The time-dependent equations have been cast within an extended Boussinesq framework in which each of the phase changes has been simulated by an enhanced thermal expansivity. Both latent heat release and viscous dissipation have been considered. Two different forms of temperature-dependent viscosity, the Arrhenius and the Frank-Kamenetzky forms, have been employed. We have considered both models with a constant temperature (equilibrium) boundary condition at the core-mantle boundary and models with a time-varying (non-equilibrium) temperature boundary condition from cooling of the core. The effects of temperature-dependent viscosity are to enhance the tendency of the convective system to be layered because of the influences of the latent heat release and the mechanical heating on creating a sharp viscosity drop across the transition zone. We have found that there is a non-linear coupling between latent heat release from the interaction of the hot plume with the endothermic phase transition and the temperature-dependent viscosity. This positive feedback process can give rise to the production of very high temperatures in the transition zone, which may cause melting in the region between the two major phase transitions. Flushing events produced by the non-equilibrium boundary condition are much more dramatic than those generated by the equilibrium boundary condition. The non-linear coupling between latent heat release and temperature-dependent viscosity is also stronger in the non-equilibrium models. Comparison with models without the presence of latent heat release and viscous dissipation shows that the models without the heating terms produce a greater degree of mass flux across the endothermic phase boundary because of the lack of the viscosity stratification in the interior of the convective flow. Results of this moded can be applied to other types of endothermic phase transition found in the lithosphere or to the spinel-perovskite transition in the deep portion of the Martian mantle.