The deformation and stress fields in an isotropic elastic circular cylinder subject to axial extension and torsion and a uniform change of temperature are shown to be governed by an integrodifferential equation that, when adapted to a recently proposed model of rubberlike thermoelasticity, has a convenient power-series solution. On this basis approximate expressions are obtained for the resultant torque and end force acting on the cylinder and for the portions of these resultants attributable to internal energy changes. Special cases are considered—notably a phenomenological analog of Flory's theory of Gaussian networks—and the paper concludes with a comparison of theoretical predictions and measurements by Boyce and Treloar of the energetic fraction of the torque on a twisted rubber cylinder.