Intrusion of magmatic bodies into continental crust has been extensively used to explain high heat flow, anomalous seismic velocity structure, and gravity anomalies. These intrusions significantly control the crustal deformation by modifying the heat and mass budget of the crust. However, thermal modeling results based on simple cooling of intrusive ignore the effect of moving boundaries during magma solidification. In the present work we discuss a mathematical formulation of the thermal evolution of continental crust in presence of such magma solidification process. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in time domain. This solution provides the cooling history and thermal evolution within an intrusion unlike the solutions proposed earlier to adjust the effect of latent heat of intrusion in the form of apparent specific heat or apparent temperature of intrusion and is a general one in the sense that this includes the radiogenic heat sources distribution and an initial depth dependent temperature distribution in lithosphere. We apply this solution to study the thermo-rheological evolution of continental lithosphere after magmatic underplating. We conclude that this effect keeps the intrusive body and the surrounding rocks at a higher temperature for a longer duration than when the effect is ignored or is adjusted in the form of increased specific heat. For an initially ductile lower crust and brittle upper mantle, magmatic underplating causes a change in the mode of deformation from brittle to ductile in the mantle layer and the latent heat effect included in the form of moving boundaries prolongs the duration of ductile deformation in this layer in comparison to the latent heat effect adjusted by increasing the specific heat of intrusion. The prolonged duration of ductility in lower crust/upper mantle due to the slow cooling of intrusion results in a weak lithosphere and is important in addressing the issues concerning crustal dynamics. ¿ American Geophysical Union 1995