In the last three years there have been a number of studies of a combined powder and wire deposition process. This technique has been shown to be applicable to a range of metallic materials, to allow high deposition rates and to be capable of creating functionally graded structures in a single pass. However, all studies to date have been of an experimental nature. In this work, the combined deposition process is analytically modelled using a method based on the Rosenthal equations that accounts for the rate and position of mass addition. The modelled quasi-stationary thermal profiles are verified by comparison with experimental data. The model makes it possible to further understand the process and compare the melt pool and temperature profiles of the conventional powder and wire feed deposition processes with the combined powder-wire process.