  We consider non-local effects which arise when radiation emitted at one
radius of an accretion disk either heats or cools gas at other radii through
Compton scattering. We discuss three situations:
  1. Radiation from the inner regions of an advection-dominated flow Compton
cooling gas at intermediate radii and Compton heating gas at large radii.
  2. Soft radiation from an outer thin accretion disk Compton cooling a hot
one- or two-temperature flow on the inside.
  3. Soft radiation from an inner thin accretion disk Compton cooling hot gas
in a surrounding one-temperature flow.
  We describe how previous results are modified by these non-local
interactions. We find that Compton heating or cooling of the gas by the
radiation emitted in the inner regions of a hot flow is not important.
Likewise, Compton cooling by the soft photons from an outer thin disk is
negligible when the transition from a cold to a hot flow occurs at a radius
greater than some minimum $R_{tr,min}$. However, if the hot flow terminates at
$R < R_{tr,min}$, non-local cooling is so strong that the hot gas is cooled to
a thin disk configuration in a runaway process. In the case of a thin disk
surrounded by a hot one-temperature flow, we find that Compton cooling by soft
radiation dominates over local cooling in the hot gas for $\dot{M} \gsim
10^{-3} \alpha \dot{M}_{Edd}$, and $R \lsim 10^4 R_{Schw}$. As a result, the
maximum accretion rate for which an advection-dominated one-temperature
solution exists, decreases by a factor of $\sim 10$, compared to the value
computed under an assumption of local energy balance.
