This article considers the scheme of a gas turbine unit (GTU) with a thermochemical exhaust heat recuperation system by using steam methane reforming. The main concept of thermochemical recuperation (TCR) is the transformation of exhaust gases heat into chemical energy of a new synthetic fuel that has higher calorimetric properties such as low-heating value. As an example, the gas turbine plants with turbines where the exhaust gas temperature exceeds 900 K are considered. To determine the optimum operating parameters of the thermochemical exhaust recuperation system, the influence of temperature, pressure, and inlet reaction mixture composition on the recuperation rate are determined. Based on thermodynamic analysis, the amount of exhaust heat that is transformed into chemical energy of the new synthetic fuel for various operating parameters is calculated. The thermodynamic analysis is performed by minimizing Gibbs energy via the programs IVTANT-HERMO and Aspen HYSYS. The results of the thermodynamic analysis are verified with the results obtained by the analytical calculation of other authors based on the law of mass action and the law of mass and energy conservation. As a result of the calculation, it was established that in the temperature range (900-1000) K the recuperation rate reaches a maximum value for the inlet reaction mixture composition of H2O: CH4 = 2; in the temperature range of above 1200 K, at H2O:CH4 = 1. It is also established that when the pressure in the reaction space increases, the energy efficiency of the use of TCR is reduced; the optimum pressure is in the range of (5-10) bar. The maximum recuperation rate of the TCR system (R = 0.693) is observed at T = 900 K, beta = 2, p = 5 bar.