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 term
s 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.
