We have performed a detailed numerical reinvestigation of the photoluminescence peak position data given by G. Oelgart &etal; [J. Appl. Phys.74, 2742 (1993)] for the ground state heavy-and light-hole excitons in a high quality molecular beam epitaxially grownGaAs/Al0.3Ga0.7Asmultiple quantum well structure. Appropriate fittings of the measured temperature dependencies of exciton peak positions from 4.2 up to 340 K are shown to be provided by a novel analytical four-parameter representation developed recently by one of the authors for the gap shrinkage effect in semiconductors. The magnitude of the limiting(T→∞)shrinkage coefficient, &agr;=0.475 meV/K, and the associated average phonon temperature, &THgr;=222.4 K, have been determined. Characteristic qualitative differences and basic deficiencies of earlier three-parameter models are discussed and illustrated numerically by comparisons with various experimental observations from low to high temperatures. ©1997 American Institute of Physics.