The two-dimensional (2D) electron energy relaxation associated with acoustic phonon emission in GaAs/Ga 1--x Al x As multiple quantum wells (MQW) has been investigated using hot-electron Shubnikov-de Haas (SdH) effect measurements performed at three different base lattice temperatures T L0 ffi 1.7, 3.5 and 5.9 K. The modulation-doped MQW samples studied have quantum well widths L Z = 51, 75 and 78 A, and only the lowest subband in each sample is populated with a 2D electron density of about 1.10 Â 10 16 m --2 . The electron temperature (T e ) has been determined from the lattice-temperature and electric-field dependencies of the amplitude of the SdH oscillations. The energy-loss rates show a power-law dependence on T e with an exponent g, which depends on T L0 . The experimental results are compared with the current theoretical models for power loss in 2D and 3D semiconductors, which include both piezoelectric and deformation-potential scattering. The electron-temperature dependence of power loss, determined experimentally at liquid-helium temperatures with T L0 ffi 1.7 K, fits well to both the 2D and 3D theoretical models in the low-temperature regime, while the results at T L0 ffi 3.5 and 5.9 K fit best to those in the intermediate-temperature regime. The results provide useful information about the relative magnitude of the deformation-potential and piezoelectric contributions to power loss.