We describe hot, optically thin solutions for one-temperature accretio
n disks around black holes. We include cooling by synchrotron, bremsst
rahlung, and Comptonization. Our solutions are thermally and viscously
stable, with gas temperatures on the order of T similar to 10(9) - 10
(10.7) K. The thermal stability is a direct result of the inclusion of
synchrotron cooling. The new solution branch is related to the advect
ion-dominated solution for a two-temperature gas, described by Narayan
& Yi (1995b). It is present only for mass accretion rates less than s
ome critical M(crit), which depends on the radius R and viscosity para
meter alpha. The solutions are advection dominated for extremely low v
alues of M. However, for a range of intermediate accretion rates, the
new solutions are both hot (T similar to 10(10) K and cooling dominate
d. Because of this new feature, one-temperature solutions are signific
antly more luminous than the corresponding two-temperature solutions a
t the same M. The radial profile of the new solutions is unusual. The
inner parts of the flow are cooling-dominated and have a disklike geom
etry, while the outer parts are fully advection-dominated and nearly q
uasi-spherical.