  We show that radiative cooling profiles, when described in temperature
coordinates, are insensitive to surface temperature $T_s$. We argue this
theoretically as well as confirm it in cloud-resolving simulations of radiative
convective equilibrium (RCE). This $T_s$-invariance holds for shortwave and
longwave cooling separately, as well as their sum. Furthermore, the
$T_s$-invariance of radiative cooling profiles leads to a simple expression for
the $T_s$-dependence of column-integrated cooling and hence precipitation, and
gives insight into why mean precipitation increases at a rate of $2 -3\%\
\mathrm{K^{-1}}$ in RCE. The relevance of these results to global climate
simulations is assessed, and the $T_s$-invariance is found to hold in the mid
and upper troposphere. In the lower troposphere, the pressure-invariance of
cloud layers and circulation tends to dominate.
