The linewidth, total integrated area, and peak position (ν0) of the intersubband transition (IT) in a GaAs/Al0.3Ga0.7As multiple quantum well, with doping in the barrier, are studied as a function of temperature using the infrared absorption technique. From the temperature dependence of the linewidth and the configuration coordinate model we find that the electrons in the GaAs well are weakly coupled to the GaAs normal optical phonon mode. The electron density (σ) in the quantum well is extracted from the total integrated area of the IT. From the temperature‐dependence of σ we conclude that the Fermi energy is also temperature dependent and that at 5 K it is about 36 meV above the ground state energy. We also find that ν0 increases as the temperature decreases. We calculated the absorption spectrum for the quantum well in a nonparabolic‐anisotropic envelope function approximation including temperature‐dependent effective masses, nonparabolicity, conduction‐band offsets, the Fermi level, and line shape broadening. Our results indicate that a large many‐body correction, in particular an exchange interaction for the ground state, is necessary to account for the experimental peak position and blue shift as the temperature is lowered.