We refer to a model of active galactic nuclei where a massive black hole (M≃108M⊙) is accreting spherically (1–3). Turbulent dissipation of the magnetic field produces an efficient heating. For low Thomson optical depth the main cooling mechanism is selfabsorbed cyclo-synchrotron (c-s) radiation from thermal electrons. The energy transfer of the thermal electrons to the c-s photons via Compton scattering (comptonization) becomes increasingly important for increasing optical depth. In ref. 2 the temperature profile of the inflowing gas was calculated balancing the heating and cooling mechanism but neglecting comptonization due to the difficulty of an analytic estimate of this process.