All previous studies of hot (T-p similar to 10(10)-10(12) K), optically thin accretion disks have neglected either the presence of e(+)e(-) pairs or advective cooling. Thus all hot disk models constructed previously have not been self-consistent. In this paper we calculate local disk models including pair physics, relevant radiative processes in the hot plasma, and the effect of advective cooling. We use a modification of the Bjornsson & Svensson mapping method. We find that the role of e(+)e(-) pairs in the structure of hot, optically thin accretion disks is far less significant than was previously thought. The improved description of the radiation-matter interactions provided in the present paper modify the previously obtained values of the critical parameters characterizing advectively dominated flows.