A coupled electroquasistatic-thermal method for the simulation of surge arresters is developed. In order to cope with the extremely short-time scales associated with the strongly nonlinear electrical characteristic of the metal–oxide resistor material, a multi-rate time integration technique is adopted. Besides, a model for the heat transfer in the arrester air gap is developed, which considers radiation and natural convection by means of an equivalent material model. 2-D finite-element simulations for a station class arrester in continuous operation are carried out and validated against measurements. Furthermore, the method is used to investigate thermal stability under pulsed overvoltages as specified by the IEC operating duty test.