  We report an inelastic neutron scattering study of the spin fluctuations in
the nearly-ferromagnetic element palladium. Dispersive over-damped collective
magnetic excitations or ``paramagnons'' are observed up to 128 meV. We analyze
our results in terms of a Moriya-Lonzarich-type spin fluctuation model and
estimate the contribution of the spin fluctuations to the low temperature heat
capacity. In spite of the paramagnon excitations being relatively strong, their
relaxation rates are large. This leads to a small contribution to the
low-temperature electronic specific heat.
