  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, $p_{\rm T}$ spectrum and
elliptic flow at low $p_{\rm T}$ 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
mid-spacetime-rapidity $|\eta|<1/2$. 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 $p_{\rm T}$ 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
$p_{\rm T}$ 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/$c$.
