An assumption on general regularities and chemical mechanisms of solid-state reactions in nanofilms and nanothermite mixtures is made. It is demonstrated that the moving force of all Al-based nanothermite reactions is the synthesis of the Al2O3 phase with a high negative enthalpy of formation. According to this assumption, all Al-based nanothermite reactions should have the same initiation temperature Tin. Indeed, an analysis of literature data shows that the synthesis of the Al2O3 phase in Al/Fe2O3, Al/CuO, Al/Co3O4, Al/MoO3, Al/Bi2O3, and Al/NiO nanothermite mixtures starts at the same temperature Tin ~ 510{\deg}C. We also demonstrate the same initiation temperatures ~250{\deg}C, ~300{\deg}C, and ~180{\deg}C for Zr-, Mg- and In-based nanothermite reactions, respectively. It is predicted that nanothermite reactions based on other fuels have their own initiation temperatures.