Temperature-dependent piezoreflectance (PzR) measurements were used to study the direct-gap-related optical transitions in a strain-compensated Ge/SiGe multiple-quantum-well (MQW) structure with Ge-rich SiGe barriers in the temperature range between 20 and 375 K. The PzR spectra revealed a wide range of possible optical transitions in the MQW structure. Detailed line-shape fits to the PzR spectra and comparison to a theoretical calculation based on the envelope-function approximation led to the identification of various interband transitions. In addition, the parameters that describe the temperature dependence of the excitonic transition energies [E(T)] and broadening parameters [Γ(T)] were evaluated and compared to those of the polar systems. In agreement with polar materials, [E(T)] values of the MQW structure were found to be similar to the constituent bulk well material. On the other hand, no significant dimensionality dependence of [Γ(T)] was observed, in contrast to polar systems. ? 2012 American Physical Society.