  The low Mach limit for 1D non-isentropic compressible Navier-Stokes flow,
whose density and temperature have different asymptotic states at infinity, is
rigorously justified. The problems are considered on both well-prepared and
ill-prepared data. For the well-prepared data, the solutions of compressible
Navier-Stokes equations are shown to converge to a nonlinear diffusion wave
solution globally in time as Mach number goes to zero when the difference
between the states at $\pm\infty$ is suitably small. In particular, the
velocity of diffusion wave is only driven by the variation of temperature. It
is further shown that the solution of compressible Navier-Stokes system also
has the same property when Mach number is small, which has never been observed
before. The convergence rates on both Mach number and time are also obtained
for the well-prepared data. For the ill-prepared data, the limit relies on the
uniform estimates including weighted time derivatives and an extended
convergence lemma. And the difference between the states at $\pm\infty$ can be
arbitrary large in this case.
