The time-dependent stress state in a representative element of a brittle fiber-reinforced linear viscoelastic material, caused by a constant temperature distribution in the cross section of the specimen, is considered. The thermo-viscoelastic stress analysis is performed by application of the correspondence principle of linear viscoelasticity to the associated thermoelastic problem. An example concerning a unit cell of a two-phase composite (silicon carbide fiber-reinforced aluminum matrix) is calculated. It may be shown that, owing to a reduction in the relaxation time of a viscoelastic material with rising temperature, the increased thermal stresses are reduced after a short time interval.