  We construct a microscopic theory of applying a heat flow from thermostatted
boundary walls in the film geometry. We treat a classical one-component fluid,
but our method is applicable to any fluids and solids. We express linear
response of any variable ${\cal B}$ in terms of the time-correlation functions
between $\cal B$ and the heat flows ${\cal J}_K$ from the thermostats to the
particles. Furthermore, the surface variables ${\cal J}_K$ can be written in
the form of space integrals of bulk quantities from the equations of motion.
Owing to this surface-to-bulk relation, the steady-state response functions
consist of dissipative and local-equilibrium parts, where the former gives rise
to Fourier's law with Green's expression for the thermal conductivity. In the
nonlinear regime, we derive the steady-state distribution in the phase space in
the McLennan-Zubarev form from the first principles. Some fluctuation theorems
are also presented.
