A temperature dependent multi-domain model is presented for numerical simulation of the electrochemical machining process with a moving cathode tool. The method includes mass transfer as a consequence of diffusion, convection and migration, combined with the electroneutrality condition and linearized temperature dependent polarization relations at the electrolyte-electrode interface. The electrolyte flow field is calculated using the laminar Navier-Stokes equations for viscous incompressible flow. Heat is generated in the bulk solution and in the electrical double layer. The electrodes are cooled by natural convection. The level set method is used for tracking the anode interface. The model is applied to the electrochemical machining of steel in a supporting electrolyte of NaNO3. Hydrogen is formed at the cathode, and metal dissolution and oxygen evolution is considered at the anode. The effect of water depletion at the electrodes is modelled by limiting the oxygen and hydrogen evolution reaction rates depending on the surface water concentration. The heat conduction through electrodes and the heat production by the electrode reactions are found to play an important role.