The studies of thermoexfoliation process in intercalation compounds Gr-SbCl5, Gr-ICI, and Gr-H2SO4 have shown that thermoexfoliation has a vivid non-linear threshold character. Experimental data are discussed within the thermodynamic theory of graphite intercalation compounds. Thermoexfoliation process takes place in the temperature range from T* to T-cr in which intercalant in GIC layers becomes unstable and the transition from the state "intercalant in GIC" into the state of pure intercalant occurs. The maximal effect of thermoexfoliation is obtained at high temperatures of thermal shock T-e, i.e, at large heating rates of the sample.