Quasiequilibrium relaxational thermodynamics is developed to understand LA-phonon-assisted thermalization of Bose-Einstein distributed excitons in quantum wells. We study quantum-statistical effects in the relaxational dynamics of the effective temperature of excitons
T=T(t). When T is less than the degeneracy temperature
T0, well-developed Bose-Einstein statistics of quantum-well excitons leads to nonexponential and density-dependent thermalization. At low bath temperatures ${T}_{b}\ensuremath{\rightarrow}0,$ the thermalization of quantum statistically degenerate excitons effectively slows down and $T(t)\ensuremath{\propto}1/\mathrm{ln}t.$ We also analyze the optical decay of Bose-Einstein distributed excitons in perfect quantum wells, and show how nonclassical statistics influences the effective lifetime ${\ensuremath{\tau}}_{\mathrm{opt}}.$ In particular, ${\ensuremath{\tau}}_{\mathrm{opt}}$ of a strongly degenerate gas of excitons is given by $2{\ensuremath{\tau}}_{R},$ where ${\ensuremath{\tau}}_{R}$ is the intrinsic radiative lifetime of quasi-two-dimensional excitons. Kinetics of resonant photoluminescence of quantum-well excitons during their thermalization is studied within the thermodynamic approach and taking into account Bose-Einstein statistics. We find density-dependent photoluminescence dynamics of statistically degenerate excitons. Numerical modeling of the thermalization and photoluminescence kinetics of quasi-two-dimensional excitons are given for ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells.