Average coronal temperature vs. optical depth. The full curves show the dependence of the average coronal temperature on the total optical depth of the corona for various values of the fraction of total power dissipated in the corona, χ, as labelled. The dashed curves represent the hydrostatic equilibrium solutions providing the largest possible Thomson depth of the Compton cooled corona for a given χ and magnetic-to-gas-pressure ratio β_m (see Sect. 6). Each of the dashed curves shows the track of the solutions in the kT_av-τ_cor plane for a fixed value of β_m (as labelled) when χ is varying.