We obtained steady solutions of optically thin, single-temperature, magnetized black hole accretion disks, assuming thermal bremsstrahlung cooling. Based on the results of 3D MHD simulations of accretion disks, we assumed that the magnetic fields inside the disk are turbulent and dominated by an azimuthal component. We decomposed the magnetic fields into an azimuthally averaged mean field and fluctuating fields. We also assumed that the azimuthally averaged Maxwell stress is proportional to the total pressure. The radial advection rate of the azimuthal magnetic flux, Phi, is prescribed as being proportional to pi(-zeta), where pi is the radial coordinate and zeta is a parameter that parameterizes the radial variation of Phi. We found that when the accretion rate, M, exceeds the threshold for the onset of the thermal instability, a magnetic pressure-dominated new branch appears. Thus, the thermal-equilibrium curve of an optically thin disk has a 'Z'-shape in the plane of the surface density and temperature. This indicates that as the mass accretion rate increases, a gas pressure-dominated optically thin hot accretion disk undergoes a transition to a magnetic pressure dominated, optically thin cool disk. This disk corresponds to the X-ray hard, luminous disk in black hole candidates observed during the transition from a low/bard state to a high/soft state. We also obtained global steady transonic solutions containing such a transition layer.