The collapse of massive rotating stellar cores and the associated accretion is thought to power long GRBs. The physical scale and dynamics of the accretion disk are initially set by the angular momentum distribution in the progenitor, and the physical conditions make neutrino emission the main cooling agent in the flow. We have carried out an initial set of calculations of the collapse of rotating polytropic cores in three dimensions, making use of a pseudo-relativistic potential and a simplified cooling prescription. We focus on the effects of self gravity and cooling on the overall morphology and evolution of the flow for a given rotation rate in the context of the collapsar model. For the typical cooling times expected in such a scenario we observe the appearance of strong instabilities on a time scale, tcool, following disk formation. Such instabilities and their gravitational interaction with the black hole (BH) produce significant variability in the energy loss and accretion rates, which would translate into neutrino cooling variations when a more realistic neutrino cooling scheme is implemented in future work.