A novel physical mechanism is proposed to explain the temperature-independent transition reactions in molecular systems. The mechanism becomes effective in the case of conformation transitions between quasi-isoenergetic molecular states. It is shown that at room temperatures, stochastic broadening of molecular energy levels predominates the energy of low-frequency vibrations accompanying the transition. This leads to a cancellation of temperature dependence in the stochastically averaged rate constants. As an example, a physical interpretation of temperature-independent onset of P2X{3} receptor desensitization in neuronal membranes is provided.