The presence of water on an oxide surface can dramatically alter its electrical properties with important consequences for electrical measurements by scanning probe microscopy, and for the use of semiconducting oxides in sensing applications. Here, the thermal dependence of the conductance of tin dioxide is interpreted by combining semiconductor equilibrium carrier statistics with a proton hopping mechanism. First, the functional form of this charge transport model is fit to experimental conductance data for tin dioxide. Next, the important energy parameters in the model are computed with density functional theory. Comparing the values of the energy parameters obtained by fitting, to the values for the same parameters obtained from electronic structure calculations, yields new insight into the surface charge transport in tin dioxide. In particular, it is found that mobile protons, freed from the dissociative adsorption of water on the [110] surface, are an essential component of the observed thermal dependence of conductance in tin dioxide.