  We consider the Navier-Stokes-Fourier system describing the motion of a
compressible, viscous and heat-conducting fluid on a domain perforated by tiny
holes. First, we identify a class of dissipative solutions to the
Oberbeck-Boussinesq approximation as a low Mach number limit of the primitive
system. Secondly, by proving the weak-strong uniqueness principle, we obtain
strong convergence to the target system on the lifespan of the strong solution.
