An investigation on the uniaxial behavior in compression and tension of an innovative Fiber-Reinforced High Toughness Cementitious Composite – FRHTCC (fc = 45 MPa at 20 °C; mostly fly ash as a binder; polyvinyl alcohol fibers; with very fine aggregate) is presented in this paper within a fairly broad thermal range (from +200 °C to −100 °C). The tests, conducted in residual conditions after each thermal cycle, indicate that sub-zero temperatures have a more detrimental effect than moderately high temperatures (the elastic-hardening behavior shifts to elastic-quasi brittle in tension at sub-zero temperatures). Based on the test results, the evolution of the strength and of the stress–strain curve in uniaxial compression is modelled by means of a damage model that assumes the Weibull distribution for concrete defects, while Ramberg-Osgood equation is introduced to describe the nonlinear behavior in tension of the material. The proposed model is shown to effectively describe damage evolution, in both compression and tension, and to realistically reproduce the stress–strain curves of the material, as demonstrated by the very good fitting of the test results. Therefore, the model is a reliable predictive tool.