A coupled semiconductor-circuit model including thermal effects is proposed. The charged particle flow in the semiconductor devices is described by the energy-transport equations for the electrons and the drift-diffusion equations for the holes. The electric circuit is modeled by the network equations from modified nodal analysis. The coupling is realized by the node potentials providing the voltages applied to the semiconductor devices and the output device currents for the network model. The resulting partial differential-algebraic system is discretized in time by the 2-stage backward difference formula and in space by a mixed-hybrid finite-element method using Marini-Pietra elements. A static condensation procedure is applied to the coupled system reducing the number of unknowns. Numerical simulations of a one-dimensional $pn$-junction diode with time-dependent voltage and of a rectifier circuit show the heating of the electrons which allows one to identify hot spots in the devices. Moreover, the choice of the boundary conditions for the electron density and energy density is numerically discussed.