It is shown that the constant-specific-heat approximation is applicable to multifractal thermodynamics of hadron-hadron and hadron-nucleus interactions at high energies. Moreover, the constant specific heats calculated from experimental data on hadron-hadron and hadron-nucleus interactions have approximately the same value for both these types of multifractal multiproduction. Thus this parameter may turn out to be an universal characteristic of the hadron-hadron and hadron-nucleus interactions. Some relationship of this phenomenon to multifractal thermodynamics at the onset of chaos is briefly discussed.