In this study, the temperature distribution of the surfaces of several substrates under an impinging gas jet from a cold spray nozzle was determined. A low-pressure cold-gas dynamic spraying unit was used to generate a jet of hot compressed nitrogen that impinged upon flat substrates. Computer codes based on a finite differences method were used to solve a simplified 2-D temperature distribution equation for the substrate to produce non-dimensional relationships between the surface temperature and the radius of the impinging fluid jet, the substrate thickness, and the heating time. It was found that a single profile of the transient non-dimensional maximum surface temperature could be used to estimate the dimensional maximum surface temperature, regardless of the value of the compressed gas temperature. It was found further that as the thermal conductance of the substrate increased, the maximum surface temperature of the substrate beneath the gas jet decreased. The close agreement of the numerical results with the experimental results suggests that the non-dimensionalized results may be applied to a wide range of conditions and materials.