Rubber technologists and engineers use the finite element method (FEM) for the analysis of stress-strain fields in deformed rubber components. In this analysis material homogeneity and isothermality of the deformations are generally assumed. Most rubber components, however, possess material non-homogeneity and undergo non-isothermal deformations. The objective of the present paper is to numerically determine the effects of the material non-homogeneity, the temperature gradient, the geometry, and the boundary rotations on the circumferential shear of a rubber tube. Computer simulations within the context of entropic finite thermoelasticity reveal that the thickness of the tube and the boundary rotations have primary effects on the stress-strain fields, whereas the effects of the temperature gradient and the material non-homogeneity are of secondary importance.