We here propose a method that, through linear transmission lines and time-domain non linear sub-circuits, solves the heat equation for one-dimensional problems in the periodic regime, involving layered structures and boundary conditions and/or media with a non-linear behavior. As an example, we provide its application to the lunar crust, represented by a layered structure, that is exposed to solar radiation and transfers heat to the sky by means of radiation. The proposed model allows then to determine the Moon temperature at different depths and in time. It represents the starting point for determining the microwave electromagnetic emission from the Moon, whose remote observation is of considerable importance in the study of its characteristics. Microwave brightness data from recent lunar missions are in good agreement with the proposed model results.