We study the structure of hot, two-temperature accretion disks around black holes, including the effects of thermal cyclo-synchrotron radiation and magnetic viscosity. This work is an extension of previous work by Björnsson & Svensson (1991a, b, 1992) and Kusunose & Mineshige (1992), which did not include those effects. Magnetic field, B, is assumed to be randomly oriented and determined by prescribing the ratio α = Pmag/Pgas or α = Pmag/(Pgas + Prad), where Pmag, Pgas, and Prad are the pressures of magnetic field, gas, and radiation, respectively. We find those effects do not change the qualitative properties of the disks, i.e., there are two critical accretion rates related to production of e± pairs, ṀcrU and ṀcrL that affect the number of local and global disk solutions, as recently found for the case with B = 0 (Björnsson & Svensson 1991a, b, 1992). However, a critical value of the α-viscosity parameter above which those critical accretion rates disappear becomes smaller than αcr = 1 found in the case of B = 0, for Pmag = α(Pgas + Prad). If Pmag = αPgas, on the other hand, αcr is still about unity. Moreover, when Comptonized cyclo-synchrotron radiation dominates Comptonized bremsstrahlung, radiation from the disk obeys a power law with the energy spectral index of ∼ 0.5, in a qualitative agreement with X-ray observations of AGNs and Galactic black hole candidates. The spectral index is weakly dependent on the mass accretion rate.