In computational models of atmospheric pressure surface barrier discharges (SBDs) the role of heating of the dielectric material and the quiescent gas is often neglected, impacting the accuracy of the calculated chemical kinetics. In this contribution, a two-dimensional fluid model of an SBD was developed and experimentally validated to determine the relative contribution of the dominant heat transfer mechanisms and to quantify the impact of discharge heating on the resultant chemistry. Three heating mechanisms were examined, including electron heating of the background gas due to inelastic collisions, ion bombardment of the dielectric surface and dielectric heating by the time-varying electric field. It was shown that electron heating of the background gas was not significant enough to account for the experimentally observed increase in temperature of the dielectric material, despite being the dominant heating mechanism of the gas close to the electrode. Dielectric heating was ruled out as the frequency response of typical dielectric materials used in SBD devices does not overlap with the experimentally observed power spectrum of an SBD excited at kHz frequencies. The ionic flux heating was found to be the dominant heating mechanism of the dielectric material and the downstream flow driven by the SBD. The largest impact of plasma heating on discharge chemistry was found in reactive nitrogen species (RNS) production, where the densities of RNSs increased when an appropriate treatment of heating was adopted. This had a marked effect on the discharge chemistry, with the concentration of NO2 increasing by almost 50% compared to the idealized constant temperature case.