Time-resolved photoluminescence (PL) and femtosecond transient absorption (TA) spectroscopy are employed to study the photoexcitation dynamics in a highly emissive two-dimensional perovskite compound (en)4Pb2Br9·3Br with the ethylene diammonium (en) spacer. We find that while the PL kinetics is substantially T-dependent over the whole range of studied temperatures T ∼ 77-350 K, the PL quantum yield remains remarkably nearly T-independent up to T ∼ 280-290 K, appreciably decreasing only at higher temperatures. Considerable differences are also revealed between the TA spectra and the responses to the excitation power at low and at room temperatures. Numerical solutions of Onsager-Braun-type kinetic-diffusion equations illustrate that the salient features of the experimental observations are consistent with the picture of a T-dependent dynamic interplay between tightly bound emissive excitons and larger-size, loosely bound, nonemissive geminate charge pairs arising already at earlier relaxation times. The geminate pairs play the role of "reservoir" states providing a delayed feeding into the emitting excitons, thus giving rise to the longer-time PL decay components and accounting for a stable PL output at lower temperatures. At higher temperatures, the propensity for thermal dissociation of excitons and bound pairs increases, leading subsequently to the precipitous decrease of the PL.