A new parameterization of the temperature and pressure dependent conductivity of mantle materials was introduced by Hofmeister in 1999. Commonly in models of the thermal state of the mantle, thermal conductivity is approximated by either a uniform value or a simple 1-D depth dependent distribution which increases monotonically with depth. In the few works including temperature dependence in mantle convection the focus has been mainly on the effect of k(T) on the character of deep mantle plumes (Matyska et al., 1994; Dubuffet et al., 2002; Sevre et al. 2002). In recent work (van den Berg et al, 2002; van den Berg and Yuen, 2002, van den Berg et al., 2004) it was shown that incorporation of the full temperature and pressure dependence into mantle convection has a significant effect on the rate of secular cooling of mantle convection models. Cooling delays of 1 to 2 Gyrs are observed, after a model evolution of some 4 Gyrs, for models with variable conductivity k(T,P), with respect to models using uniform k of similar volume average k value. This has been observed both in isoviscous models and in models including temperature and pressure dependent viscosity with temperature contrast of the viscosity up to 30000. In the present talk I will show results of these experiments and also more recent work including thermal coupling between the mantle and core which illustrates that variable T,P dependent thermal conductivity is a significant factor in controling core cooling and therefore also important for the history of the Earth's magnetic field.