  Atmospheric heat redistribution shapes the remote appearance of rocky
exoplanets but there is currently no easy way to predict a planet's heat
redistribution from its physical properties. This paper proposes an analytical
scaling theory for the heat redistribution on tidally-locked rocky exoplanets.
The main parameters of the scaling are a planet's equilibrium temperature,
surface pressure, and broadband longwave optical thickness. The scaling
compares favorably against idealized general circulation model simulations of
TRAPPIST-1b, GJ1132b, and LHS 3844b. For these planets heat redistribution
generally becomes efficient, and a planet's observable thermal phase curve and
secondary eclipse start to deviate significantly from that of a bare rock, once
surface pressure exceeds O(1) bar. The scaling additionally points to planetary
scenarios for which heat transport can be notably more or less efficient, such
as H2 and CO atmospheres or hot lava ocean worlds. The results thus bridge the
gap between theory and imminent observations with the James Webb Space
Telescope. They can also be used to parameterize the effect of 3D atmospheric
dynamics in 1D models, thereby improving the self-consistency of such models.
