One of the most interesting results obtained in the study of mechanical properties of binary and multicomponent solid solutions (high-entropy alloys, HEAs) is the presence of long athermic hardening, which causes the appearance of a characteristic ‘plateau’ on the curve of temperature dependence of critical shear stress $\tau_{\textrm{cr}}$($T$) (or yield strength $\sigma_{0.2}$($T$)) at temperatures above 0.2–0.35$T_{\textrm{m}}$. From the point of view of creation of the new materials, that are able to withstand mechanical loads at high temperatures, determining mechanisms for the appearance of such a ‘plateau’ is extremely actual. In the presented work the existing representation about the features of the temperature dependence of the critical shear stress in binary and multicomponent solid solutions are considered in comparison with pure metals. A new approach for determining the nature of athermal ‘plateaus’ on the curves of temperature dependences of the critical shear stress $\tau_{\textrm{cr}}$($T$) is proposed. As shown, the existence of a ‘plateau’ in the $\tau_{\textrm{cr}}$($T$) dependence in solid solutions and in pure metals at the indicated temperatures is, in fact, anomalous, since with an increase in temperature there is a noticeable decrease in their Young’s modulus, which, respectively, should also lead to a decrease in the critical shear stress $\tau_{\textrm{cr}}$. The authors’ analysis indicates that the factor that compensates for the expected decrease in $\tau_{\textrm{cr}}$ associated with a decrease in the elastic modulus in pure metals is an increase in the mean square displacements of atoms from ideal positions in the crystal lattice as a result of a linear increase in dynamic distortions of the crystal lattice with increasing temperature. In multicomponent solid solutions, in addition to an increase in the mean square displacements of atoms, the dependence $\tau_{\textrm{cr}}$($T$) in the temperature range where a ‘plateau’ is observed, effects similar to dynamic deformation aging, which are accompanied by unequal mobility of atoms of different elements, can also affect. The results obtained can be used to select the elemental composition of multicomponent heat-resistant alloys, which will be competitive in comparison with the known traditional alloys.