  We prove that $(\lambda_g\mapsto e^{-t|g|^r}\lambda_g)_{t>0}$ defines a
completely bounded semigroup of multipliers on the von Neuman algebra of
hyperbolic groups for all real number $r$. One ingredient in the proof is the
observation that a construction of Ozawa allows to characterize the radial
multipliers that are bounded on every hyperbolic graph, partially generalizing
results of Haagerup--Steenstrup--Szwarc and Wysocza\'nski. Another ingredient
is an upper estimate of trace class norms for Hankel matrices, which is based
on Peller's characterization of such norms.
