Recent interferometric synthetic aperture radar observations over northern Alberta, Canada, show persistent surface heave occurring at rates of 1-4 cm/yr, localized at sites where the steam-assisted gravity drainage technique is currently used to extract bitumen from the Athabasca oil sands. We find that uplift rates above the horizontal injector wells are strongly correlated with rates of steam injection, even though there is a net fluid loss from the reservoir pore space as oil and water are withdrawn through the production wells. In combination with available steam injection and bitumen production data at four sites, we use reservoir flow models to explain how the thermal and geomechanical effects of steam injection on an oil sand reservoir can generate uplift at the surface. Results of our numerical experiments show that persistent surface heave consistent with observed rates can be driven by stress changes in the reservoir due to porous flow and thermal expansion. We also observe an unexpected localized uplift, of magnitude equal to or greater than the heave above the sites of steaming but located at clusters of wellheads which are outside the region of influence of the steam chambers. We show that this "wellhead" deformation can be explained by thermal expansion of rock near the injector wells.