  We investigate the magnetic and the transport properties of diluted magnetic
semiconductors using a spin-fermion Monte-Carlo method on a 3D lattice in the
intermediate coupling regime. The ferromagnetic transition temperature $T_c$
shows an optimization behavior, first increases and then decreases, with
respect to the absolute carrier density $p_{abs}$ for a given magnetic impurity
concentration $x$, as seen in the experiment. Our calculations also show an
insulator-metal-insulator transition across the optimum $p_{abs}$ where the
$T_c$ is maximum. Remarkably, the optimum $p_{abs}$ values lie in a narrow
range around 0.11 for all $x$ values and the ferromagnetic $T_c$ increases with
$x$. We explain our results using the polaron percolation mechanism and outline
a new route to enhance the ferromagnetic transition temperature in experiments.
