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., $\dot{M}\la 10��^2\dot{M}_{\rm Edd}$, where $\dot{M}_{\rm Edd}= L_{\rm Edd}/c^2$ is the Eddington accretion rate. At low mass flow rates, $\dot{M}\la 10^{-3}��^2 \dot{M}_{\rm Edd}$, 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.

24 pages, 8 figures, to appear in ApJ