Following the observational and theoretical evidence that points at core collapse supernovae as major producers of dust, 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 supernova 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 supernova era (~ 3 Myr - 40 Myr). Such a balance determines the range of dust to gas mass ratio and this the dust cooling law. We then search for the critical line in the cluster mechanical luminosity (or cluster mass) vs cluster size, that separates quasi- adiabatic and strongly radiative cluster wind solutions from the bimodal cases. 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\infty, lower than when only gas radiative cooling is applied. And thus, massive clusters (M_sc > 10^5 Msun) are predicted to enter the bimodal regime.