  The effectiveness of the thermal coupling of ions and electrons in the
context of optically thin, hot accretion flows is investigated. In the limit of
complete coupling, we focus on the one-temperature accretion flows. Based on a
global analysis, the results are compared with two-temperature accretion flow
models and with the observations of black hole sources. Many features are quite
similar. That is, hot one-temperature solutions are found to exist for mass
flow rates less than a critical value; i.e., $\dot{M}\la 10\alpha^2\dot{M}_{\rm
Edd}$, where $\dot{M}_{\rm Edd}= L_{\rm Edd}/c^2$ is the Eddington accretion
rate. At low mass flow rates, $\dot{M}\la 10^{-3}\alpha^2 \dot{M}_{\rm Edd}$,
the solution is in the advection-dominated accretion flow (ADAF) regime. But at
higher rates, radiative cooling is effective and is mainly balanced by
advective {\em heating}, placing the solution in the regime of luminous hot
accretion flow (LHAF). To test the viability of the one-temperature models, we
have fitted the spectra of the two black hole sources, Sgr A* and XTE
J1118+480, which have been examined successfully with two-temperature models.
It is found that the one-temperature models do not provide acceptable fits to
the multi-wavelength spectra of Sgr A* nor to XTE J1118+480 as a result of the
higher temperatures characteristic of the one-temperature models. It is
concluded that the thermal coupling of ions and electrons cannot be fully
effective and that a two-temperature description is required in hot accretion
flow solutions.
