We present a new method to predict the power losses in electric vehicle (EV) transmission systems using a thermally coupled gearbox efficiency model. Friction losses in gear teeth contacts are predicted using an iterative procedure to account for the thermal coupling between the tooth temperature, oil viscosity, film thickness, friction, and oil rheology during a gear mesh cycle. Crucially, the prediction of the evolution of the coefficient of friction (COF) along the path of contact incorporates measured lubricant rheological parameters as well as measured boundary friction. This allows the model to differentiate between nominally similar lubricants in terms of their impact on EV transmission efficiency. Bearing and gear churning losses are predicted using existing empirical relationships. The effects of EV motor cooling and heat transfers in the heat exchanger on oil temperature are considered. Finally, heat transfer to the surroundings is accounted for so that the evolution of gearbox temperature over any given drive cycle can be predicted. The general approach presented here is applicable to any automotive gearbox while incorporating features specific to EVs. The model predictions are compared to real road measurements made on a popular current EV, and good agreement is shown over a range of road conditions. It should be noted that at high input speeds, the current model somewhat overpredicts the gearbox losses due to limitations in existing empirical bearing and churning loss models. Analyses of transmission losses breakdown at constant input power show that at low speeds/high torques, it is the losses in the gear meshes and high-load bearings that are most significant whereas at high speeds/low torques the losses in high-speed input shaft bearings, as well as gear churning losses, become more important. It is shown that the gearbox losses can account for 15-25% of the overall power losses in an EV depending on road conditions; a much higher proportion than in an internal combustion engine (ICE) vehicle, thus demonstrating that reducing transmission losses offers an important avenue for improving EV efficiency. Finally, the influence of oil properties on EV transmission losses is demonstrated by applying the model to predict losses over the Worldwide Harmonized Light Vehicles Test Procedure (WLTP) drive cycle. The presented model can help to optimize both gearbox design and lubricant properties to minimize EV transmission losses and hence improve EV range.