The influences of variations in thermal conductivity due to composition, temperature, and pressure in mantle and crust on the thermochemical evolution of Mars have been examined with parameterized convection models. We use a temperature- and pressure-dependent thermal conductivity in the mantle and column-averaged values between 1.5 and 4 Wm-1K-1 for the crust (with 2 Wm-1K-1 as the representative value for a basaltic crust). The major characteristic of the models is a slower cooling of the upper mantle with a long-existing global partial melt zone and a stronger crustal production late in the evolution compared to earlier models which assume a constant thermal conductivity of 4 Wm-1K-1. To explain the observed crustal thickness and the early crustal formation on Mars, the formation of an enriched primordial crust is required. Recent volcanism can be explained by lateral temperature variations that are caused by thickness variations of the low conducting crust. These melt zones which occur underneath thicker than average crust may be the source region for the observed longstanding volcanism in Tharsis and Elysium instead of plumes rising from the core-mantle boundary. The evolution of the elastic lithosphere is characterized by a transition at which the elastic strength is first provided by the crust and later also by the upper mantle. This finding may explain the estimated elastic lithosphere thickness of less than 16 km in the Noachian and more than 100 km in the Hesperian and Amazonian.