  In the present work, motivated by the studies on the low Mach number limit
problem, we establish uniform regularity estimates with respect to the Mach
number for the non-isentropic compressible Navier-Stokes system in smooth
domains with Navier-slip boundary conditions, in the general case of
ill-prepared initial data. The thermal conduction is taken into account and the
large variation of temperature is allowed. Moreover, the obtained regularity
estimates are also uniform in the Reynolds number $\text{Re}\in[1,+\infty),$
P\'eclet number $\text{Pe}\in [1,+\infty),$ provided
$$\big|\frac{1}{\text{Re}}-\frac{\iota_0}{\text{Pe}}\big|\lesssim
\frac{1}{\text{Pe}^{\frac{1}{2}}}\frac{1}{\text{Re}},$$ where $\iota_0$ is a
fixed constant independent of the Mach number, Reynolds number, and P\'eclet
number. The large temperature variation as well as the interactions of two
kinds of boundary layers are the main obstacles to the proof.
