In this paper, we speculate on the possibility of the existence of a clustered thick disc-like component of dark matter in the Milky Way. We calculate the heating rate of the stellar disc embedded in such a dark disc made up of massive clusters, as a result of gravitational scattering. There is a region of parameter space of massive clusters (~10^6 M_solar) satisfying observational and dynamical constraints for which such a component would contribute significantly to the heating of the disc without a sensible destruction of the three-dimensional globular cluster system. Little observable heating by dark clusters in the solar neighbourhood is produced in the case of a local (number cluster per unit area x mass of a cluster squared) <8 x 10^6 M_solar^2pc^-2. For other galaxies, this scenario may allow the stellar velocity dispersion to have different age dependences such as, for example, that recently suggested for IC 2531. Other consequences on the galactic discs are also discussed.