Crystals having a gap in a phonon spectrum can support so-called gap discrete breathers (DBs), i.e., nonlinear localized vibrational modes existing in perfect crystals and having frequencies within the gap. In our recent work, for a two-dimensional crystal with stoichiometry A3B, we have demonstrated that if the atomic weight of the components is related as MA MB , then there is a wide gap in the phonon spectrum and the gap DBs can be easily excited. The situation is opposite if the above condition is not satisfied. In the present work the gap DBs are studied at thermal equilibrium, whereas in the previous study the temperature was zero. We demonstrate that in the crystal supporting DBs, in contrast to the opposite case, the lifetime of high-energy light atoms grows with temperature. The possible role of gap DBs in the thermally activated formation of vacancy and interstitial atom pairs (Frenkel pairs) was studied. We have measured the time needed for the appearance of a Frenkel pair as a function of temperature for the crystals supporting and not supporting DBs. A minor difference in waiting time of Frenkel pair nucleation was found in these two cases. We argue that, for the model and its parameters considered in the present work, the main mechanism of thermally activated Frenkel pair formation is the cooperative motion of atoms rather than the excitation of DBs.