The stability of the geometrically thin, two-temperature hot accretion disk is studied. The general criterion for thermal instability is derived from the linear local analyses, allowing for advective cooling and dynamics in the vertical direction. Specifically, classic unsaturated Comptonization disk is analysed in detail. We find five eigen-modes: (1) Heating mode grows in thermal time scale, $(5/3)({alpha}{omega})^{-1}$, where alpha is the viscosity parameter and w the Keplerian frequency. (2) Cooling mode decays in time scale, $(2/5)(T_e/T_i)({alpha}{omega})^{-1}$, where $T_e;and;T_i$ are the electron and ion temperatures, respectively. (3) Lightman-Eardley viscous mode decays in time scale, $(4/3)(Lambda/H)^2({alpha}{omega})^{-1}$, where $Lambda$ is the wavelength of the perturbation and H the unperturbed disk height. (4) Two vertically oscillating modes oscillate in Keplerian time scale, $(3/8)^{1/2}omega^{-1}$ with growth rate $propto;(H/Lambda)^2$. The inclusion of dynamics in the vertical direction does not affect the thermal instability, adding only the oscillatory modes which gradually grow for short wavelength modes. Also, the advective cooling is not strong enough to suppress the growth of heating modes, at least for geometrically thin disk. Non-linear development of the perturbation is followed for simple unsaturated Compton disk: depending on the initial proton temperature perturbation, the disk can evolve to decoupled state with hot protons and cool electrons, or to one-temperature state with very cool protons and electrons.