Following the observational and theoretical evidence that points at core-collapse supernovae (SNe) as major producers of dust, here we calculate the hydrodynamics of the matter reinserted within young and massive super stellar clusters under the assumption of gas and dust radiative cooling. The large SN rate expected in massive clusters allows for a continuous replenishment of dust immersed in the high temperature thermalized reinserted matter and warrants a stationary presence of dust within the cluster volume during the type II SN era. We first show that such a balance determines the range of the dust-to-gas-mass ratio, and thus the dust cooling law. We then search for the critical line that separates stationary cluster winds from the bimodal cases in the cluster mechanical luminosity (or cluster mass) versus cluster size parameter space. In the latter, strong radiative cooling reduces considerably the cluster wind mechanical energy output and affects particularly the cluster central regions, leading to frequent thermal instabilities that diminish the pressure and inhibit the exit of the reinserted matter. Instead, matter accumulates there and is expected to eventually lead to gravitational instabilities and to further stellar formation with the matter reinserted by former massive stars. The main outcome of the calculations is that the critical line is almost two orders of magnitude or more, depending on the assumed value of V A∞, lower than when only gas radiative cooling is applied. And thus, many massive clusters are predicted to enter the bimodal regime.