The present study takes the CoRoT-7b exoplanet as an analogue for massive terrestrial planets to investigate conditions, under which intrinsic magnetic fields could be sustained in liquid cores. We examine the effect of depth-dependent transport parameters (e.g., activation volume of mantle rock) on a planet's thermal structure and the related heat flux across the core mantle boundary. For terrestrial planets more massive than the Earth, our calculations suggest that a substantial part of the lowermost mantle is in a sluggish convective regime, primarily due to pressure effects on viscosity. Hence, we find substantially higher core temperatures than previously reported from parameterized convection models. We also discuss the effect of melting point depression in the presence of impurities (e.g., sulfur) in iron-rich cores and compare corresponding melting relations to the calculated thermal structure. Since impurity effects become less important at the elevated pressure and temperature conditions prevalent in the deep interior of CoRoT-7b, iron-rich cores are likely solid, implying that a self-sustained magnetic field would be absent.