In addition to the results of our own experiments on the decompositions of calcite crystals under high-vacuum (10(-8) bar) and low-vacuum (10(-2) bar) conditions, some data reported in the literature were used for the determination of the E parameters by the second- and third-law methods and discussion of the self-cooling effect on the results of these determinations. Analysis of these data supports the advantages of the third-law method compared with the second-law (and Arrhenius-plots) methods in relation to reliability of results obtained. The experimental values of the E parameters, obtained by different technique and under different conditions by the third-law method, are in excellent agreement with the theoretically predicted values based on the mechanism of congruent decomposition of CaCO3 into gaseous species CO2 and CaO with the simultaneous condensation of low-volatility CaO molecules. Indeed, the experimental values of the E parameters in the equimolar and isobaric modes of decomposition, obtained in this work under optimal conditions, are equal to 261 and 493 kJ mol(-1), respectively whereas the theoretical values at these temperatures equals to 253 and 505 kJ mol(-1). The application of the third-law method allowed to support the enormous influence of self-cooling on the results obtained by the usual second-law and Arrhenius-plots methods accepted in thermal analysis. The role of this effect is increased dramatically in the experiments performed under high-vacuum conditions. Contrary to the second-law method, the third-law method appears to be rather insensitive to reactant self-cooling in the process of decomposition and to the presence of gaseous product (CO2) in the reactor.