I study the space-time evolution of transverse flow and effective temperatures in the dense parton phase with the string melting version of a multi-phase transport model. Parameters of the model are first constrained to reproduce the bulk data on the rapidity density, p_ T spectrum and elliptic flow at low p_ T for central and mid-central Au+Au collisions at 200A GeV and Pb+Pb collisions at 2760A GeV. I then calculate the transverse flow and effective temperatures in volume cells within

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... etime-rapidity |η|<1/2. I find that the effective temperatures extracted from different variables, which are all evaluated in the rest frame of a volume cell, can be very different; this indicates that the parton system in the model is not in full chemical or thermal equilibrium locally, even after averaging over many events. In particular, the effective temperatures extracted from the parton energy density or number density are often quite different than those extracted from the parton mean p_ T or mean energy. For these collisions in general, effective temperatures extracted from the parton energy density or number density are higher than those extracted from the parton mean p_ T in the inner part of the overlap volume, while the opposite occurs in the outer part of the overlap volume. I argue that this indicates that the dense parton matter in the inner part of the overlap volume is over-populated; I also find that all cells with energy density above 1 GeV/fm^3 are over-populated after a couple of fm/c.