  We compute the counterterms necessary for the renormalization of the one-loop
effective action of massive gravity from a worldline perspective. This is
achieved by employing the recently proposed massive $\mathcal{N}=4$ spinning
particle model to describe the propagation of the massive graviton on those
backgrounds that solve the Einstein equations without cosmological constant,
namely on Ricci-flat manifolds, in four dimensions. The model is extended to be
consistent in $D$ spacetime dimensions by relaxing the gauging of the full
SO(4) R-symmetry group to a parabolic subgroup, together with the inclusion of
a suitable Chern-Simons term. Then, constructing the worldline path integral on
the one-dimensional torus allows for the correct calculation of the one-loop
divergencies in arbitrary $D$ dimensions. Our primary contribution is the
determination of the Seleey-DeWitt coefficients up to the fourth coefficient
$a_3(D)$, which to our knowledge has never been reported in the literature. Its
calculation is generally laborious on the quantum field theory side, as a
general formula for these coefficients is not available for operators that are
non-minimal in the heat kernel sense. This work illustrates the computational
efficiency of worldline methods in this regard. Heat kernel coefficients
characterize linearized massive gravity in a gauge-independent manner due to
the on-shell condition of the background on which the graviton propagates. They
could serve as a benchmark for verifying alternative approaches to massive
gravity, and, for this reason, their precise expression should be known
explicitly.
