Currently, microwave is one of the most interesting ways to conduct drying of dielectric materials, in particular coal. In this paper, two processes were considered - heating and drying. The temperature field of the coal semi-mass in the heating mode is found analytically strictly with the use of integral transformations. The drying process is formulated as a nonlinear Stephen problem with a moving boundary of the liquid-vapor phase transformation. The temperature distribution, speed and drying time in this mode are determined approximately analytically. Parametric analysis of the influence of the material and boundary conditions on the dynamics of warming up and drying is revealed.