  We study the dynamics of two-component atomic Bose gases initially in a
mixture encountering a sudden quench of the inter-species interactions. The
dynamics above the critical temperature $T_c$ is studied using a leading order
large-N approximation that predicted a phase transition from mixing to phase
separation as a function of the inter-species coupling. Here we explore the
dynamics of this phase transition following a quench and compare our results to
those found at zero temperature using the time-dependent Gross-Pitaevskii
equations which ignore quantum and thermal fluctuations. In the regime above
$T_c$ where no condensate is present, however, the time evolution of the
densities following the quench exhibits features similar to that found at zero
temperature where only the condensates contribute to the densities. When the
inter-species interaction jumps above the critical value, we observe dynamical
transitions from a homogeneous mixture to a phase-separated structure for both
cases. Our simulations suggest that at temperatures above $T_c$ where no
condensate is present this dynamical transition should still be observable in
experiments.
