The dynamic strength of concrete subjected to variable thermal and velocity conditions is examined, predicated on the incubation time criterion and the thermal fluctuation theory of strength. A salient feature of this criterion is the invariant characteristic time, serving as a quantification of the loading rate. Model validation is accomplished through a comparative analysis of predicted outcomes against empirical data obtained from concrete specimens incorporating basalt, gravel, and limestone aggregates. It is shown that the characteristic relaxation time of concretes increases within the temperature interval of 20 to 800 °C and decreases at temperatures above ~ 800 °C. The temperature dependence of the characteristic relaxation time for concrete with basalt, limestone and gravel aggregate, determining the intensity of the relaxation process, is predicted based on proposed model.