  We study the zero viscosity and heat conductivity limit of an initial
boundary problem for the linearized Navier-Stokes-Fourier equations of a
compressible viscous and heat conducting fluid in the half plane. We consider
the case that the viscosity and thermal diffusivity converge to zero at the
same order. The approximate solution of the linearized Navier-Stokes-Fourier
equations with inner and boundary expansion terms is analyzed formally first by
multiscale analysis. Then the pointwise estimates of the error terms of the
approximate solution are obtained by energy methods, thus establish the uniform
stability for the linearized Navier-Stokes-Fourier equations in the zero
viscosity and heat conductivity limit. This work is based on \cite{xy} and
generalize the results from isentropic case to the general compressible fluid
with thermal diffusive effect. Besides the viscous layer as in \cite{xy},
thermal layer appears and coupled with the viscous layer linearly.
