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Surface-mounted heated films have been used for fluid-flow measurement for many years. Recently unsteady heating of such surface films has been explored experimentally. In this paper steady-periodic heating of a surface-mounted film is studied analytically. Wall effects and axial heat conduction in the fluid are included. The temperature is found as an exact integral expression constructed from separate Green’s function formulations in the fluid flow and in the solid wall that are matched at the fluid-solid interface. Results for temperature, obtained by quadrature, are reported for several flow speeds and several steady-periodic frequencies. The results show that steady-periodic heating has potential for shear-stress measurement because the heating frequency may be tuned to maximize the temperature response at the shear stress of interest. Thermal calibration of these sensors is discussed, and simulated calibration curves are given.