A method of calculating the steady-state operating temperature of a shielded magnetoresistive element in three dimensions is described. The method of images is used to account for any number of layers of different thermal conductivities, which may include, for example, gaps, shields, undercoat, overcoat, and substrate. The temperature may be calculated at any point, allowing the average temperature of the stripe to be calculated. The effect of the thermal coefficient of resistance is included. Results of calculations using the model compare favorably to measurements.