The present paper studies the effects of curvilinear material anisotropy on the temperature distributions of thin walled bodies of revolution. To facilitate the analysis, the thinness property of shells is used to develop an approximate three-dimensional anisotropic heat conduction equation and associated boundary conditions for thin walled bodies of revolution. Based on these equations, a solution procedure is developed by means of successive integral transforms and subsequent numerical integration. Using the integral transforms, a solution is obtained for temperature distributions in cylindrical thin walled bodies. In terms of this solution, the effects of cylindrical anisotropy on the temperature distribution is discussed at length.