  We investigate the metal insulator transitions at finite temperature for the
Hubbard model with diagonal alloy disorder. We solve the dynamical mean field
theory equations with the non crossing approximation and we use the coherent
potential approximation to handle disorder. The excitation spectrum is given
for various correlation strength $U$ and disorder. Two successive metal
insulator transitions are observed at integer filling values as $U$ is
increased. An important selective transfer of spectral weight arises upon
doping. The strong influence of the temperature on the low energy dynamics is
studied in details.
