The article studies the influence of steel fiber on the change in temperature stresses in concrete at an early hardening stage. When hardening concrete is exposed to heat treatment, its volume and, consequently, density change. Under certain circumstances, this can lead to its structural damage and, ultimately, to a decrease in its physical and mechanical properties at the design age. Such structural damage of concrete can appear even at the earliest hardening stage, before the formation of the elastic properties of the material. When testing concretes subjected to heating, we recorded the development of temperature deformations and assessed their plastic viscosity. To determine the temperature stresses, we proposed a method based on the Kelvin-Voigt rheological model. Studies have shown that the presence of steel fibers in concrete leads to a decrease in the deformations of concrete during heat treatment. To assess the thermal stresses arising at the early stage of hardening, we derived an analytical dependence, taking into account the viscosity of the hardening concrete. During the experiments, we obtained values for the viscosity of steel-fiber reinforced concrete depending on its fiber content. The results showed that, without changing its density, steel-fiber reinforced concrete can take significantly higher thermal stresses than unreinforced concrete at the early hardening stages. With an increase in the temperature, the change in the thermal stresses, depending on the fiber content, begins to have a more pronounced non-linear nature. We also showed that before a certain structural strength is reached, there are no thermal stresses in steel-fiber reinforced concrete due to the steel-fiber induced redistribution of temperature forces throughout the volume of concrete.