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In the present work, motivated by the studies on the low Mach number limitproblem, we establish uniform regularity estimates with respect to the Machnumber for the non-isentropic compressible Navier-Stokes system in smoothdomains with Navier-slip boundary conditions, in the general case ofill-prepared initial data. The thermal conduction is taken into account and thelarge variation of temperature is allowed. Moreover, the obtained regularityestimates 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 afixed constant independent of the Mach number, Reynolds number, and P\'ecletnumber. The large temperature variation as well as the interactions of twokinds of boundary layers are the main obstacles to the proof.

Uniform regularity in the low Mach number and inviscid limits for the full Navier-Stokes system in domains with boundaries