  The global existence issue in critical regularity spaces for the full
Navier-Stokes equationssatisfied by compressible viscous and heat-conductive
gases has been first addressed in \cite{D2}, then recently extended to the
general $L^p$ framework in \cite{DH}.In the present work, we establish decay
estimates for the global solutions constructed in \cite{DH}, under anadditional
mild integrability assumption that is satisfied if the low frequencies of the
initial data are in $L^{p/2}({\mathbb{R}}^d).$As a by-product we recover in
dimension three the classical decay rate $t^{-\frac34}$ for $t\to+\infty$ that
has been observed by A. Matsumura and T. Nishida in \cite{MN2} for solutions
with high Sobolev regularity. Compared to a recent paper of us \cite{DX}
dedicated to the barotropic case, not only we are able to treat the full
system, but we also improve the decay rates for the high frequencies of the
solution. We believe the correspondant decay exponents to be optimal.
