In order to design coated fiber for optical frequency domain reflectometer (OFDR) temperature sensing, improve the temperature sensitivity of OFDR and increase its applicable scenarios, this paper theoretically analyzes and simulates the effects of one and two layers of coating on the temperature sensitivity of Rayleigh frequency shift in single-mode fiber. Firstly, the effects are analyzed by using the Lame solution theory in term of the geometrical, thermal and mechanical properties of the coating. Secondly, a simplified solution with only one layer of coating is proposed based on the relationship of axial strain in optical fiber caused by temperature and the force balance between optical fiber and one layer of coating. Finally, the temperature sensitivity of Rayleigh frequency shift of the one-layer and two-layer coated optical fiber is simulated on the basis of the established theoretical model. The results show that the sensitivity increases with the increase of Young's modulus, radius and thermal expansion coefficient of the outer coating. However, it is almost independent of Poisson's ratio of the coating. The results of this paper could broaden the application of OFDR in high temperature sensitive and cryogenic temperature scenarios.