  Among heavy-fermion metals, Ce$_3$Pd$_{20}$Si$_6$ is one of the
heaviest-electron systems known to date. Here we used high-resolution neutron
spectroscopy to observe low-energy magnetic scattering from a single crystal of
this compound in the paramagnetic state. We investigated its temperature
dependence and distribution in momentum space, which was not accessible in
earlier measurements on polycrystalline samples. At low temperatures, a
quasielastic magnetic response with a half-width {\Gamma}=0.1 meV persists with
varying intensity all over the Brillouin zone. It forms a broad hump centered
at the (111) scattering vector, surrounded by minima of intensity at (002),
(220) and equivalent wave vectors. The momentum-space structure distinguishes
this signal from a simple crystal-field excitation at 0.31 meV, suggested
previously, and rather lets us ascribe it to short-range dynamical correlations
between the neighboring Ce ions, mediated by the itinerant heavy f-electrons
via the RKKY mechanism. With increasing temperature, the energy width of the
signal follows the conventional T$\scriptstyle^{1/2}$ law, {\Gamma}(T) =
{\Gamma}$_0$ + A*T$\scriptstyle^{1/2}$. The momentum-space symmetry of the
quasielastic response suggests that it stems from the simple-cubic Ce
sublattice occupying the 8c Wyckoff site, whereas the crystallographically
inequivalent 4a site remains magnetically silent in this material.
