An approximate analytical theory is developed to describe the effects of temperature on the birefringence in a coated stress-induced birefringent optical fiber. Because of the mismatch in the thermal expansion coefficients of the cladding and the stress-applying sections in the fiber, the birefringence in the fiber responds directly to a change of temperature. Additional changes in the birefringence can be produced indirectly by the temperature-induced radial stress and axial strain in the glass fiber through the fiber coating. Depending on the coating material and thickness as well as the thermoelastic properties of the fiber glasses, the indirect effect can reinforce or cancel the direct effect. It is possible to design a fiber with a birefringence that is insensitive to temperature variation over a range of temperature. Expressions suitable for fiber design are presented. Both plastic and metal coating materials are considered. Design examples for boron-doped fibers are given.