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In the current work, a new generalized model of heat conduction has been constructed taking into account the influence of the microscopic structure into the on non-simple thermoelastic materials. The new model was established on the basis of the system of equations that includes three-phase lags of higher-order and two different temperatures, namely thermodynamic and conductive temperature. The two-temperature thermoelastic model presented by Chen and Gurtin (Z Angew Math Phys 19(4)614-627, 1968) and some other previous models have been