This paper presents a weakly coupled formulation for the electromagnetic and thermal fields by applying the backward differentiation formula (BDF) and the Theta algorithm for the adaptive time-stepping and variable order 2D finite-element discretization. A coupling of the electromagnetic diffusion equation (EDE) and the electrical circuit equations is also included. A minimum time step criterion is adopted and an algorithm for the time-step size and order selection is implemented. The proposed model was programmed in C language. An example is presented to show the application of the formulation.