We have developed a thermodynamic model for the determination of the temperature profile based on the balance of radiative and turbulent fluxes. In the context of a one-dimensional case, we show that the temperature field is governed by a first-order differential-integro equation involving temperature to the fourth power. In conjunction with the temperature profile determination, parameterization programs for the transfer of broadband thermal infrared and solar fluxes in inhomogeneous atmospheres are developed. In addition, the vertical transport is parameterized using a first-order closure scheme with the eddy thermal diffusion coefficients derived either from known theories or from available data. By virtue of an efficient perturbation technique devised for the solution of the thermal equilibrium temperature, we show that the simulated temperatures compare well with those of a standard atmosphere employing climatological water vapor, ozone and cloud profiles. Simulations using the steady-state ... Abstract We have developed a thermodynamic model for the determination of the temperature profile based on the balance of radiative and turbulent fluxes. In the context of a one-dimensional case, we show that the temperature field is governed by a first-order differential-integro equation involving temperature to the fourth power. In conjunction with the temperature profile determination, parameterization programs for the transfer of broadband thermal infrared and solar fluxes in inhomogeneous atmospheres are developed. In addition, the vertical transport is parameterized using a first-order closure scheme with the eddy thermal diffusion coefficients derived either from known theories or from available data. By virtue of an efficient perturbation technique devised for the solution of the thermal equilibrium temperature, we show that the simulated temperatures compare well with those of a standard atmosphere employing climatological water vapor, ozone and cloud profiles. Simulations using the steady-state ...