The linewidth and peak position (vo) of the intersubband transition (IT) in GaAs/Al0.3Ga0.7As multiple quantum wells are studied as a function of temperature using the infrared absorption technique. We find that electrons in the GaAs well are weakly coupled to the GaAs normal optical phonon mode. The total integrated area of IT absorption is found to be approximately constant in the samples that were doped in the well but temperature dependent in the samples that were doped in the barrier. We also find that vo increases as the temperature decreases. This blue shift is found to increase as the dopant concentration is increased. We calculated the absorption spectrum in a nonparabolic-anisotropic envelope function approximation including temperature dependent effective masses, nonparbolicity, conduction band offsets, the Fermi level, and lineshape broadening. Our results indicate that a large manybody correction, in particular an exchange interaction (Eexch) for the ground state, is necessary to account for the observed blue shift as the dopant concentration increases.