We study the influence of spatial confinement on the second-order temporal coherence of the emission from a semiconductor microcavity in the strong coupling regime. The confinement, provided by etched micropillars, has a favorable impact on the temporal coherence of solid state quasicondensates that evolve in our device above threshold. By fitting the experimental data with a microscopic quantum theory based on a quantum jump approach, we scrutinize the influence of pump power and confinement and find that phonon-mediated transitions are enhanced in the case of a confined structure, in which the modes split into a discrete set. By increasing the pump power beyond the condensation threshold, temporal coherence significantly improves in devices with increased spatial confinement, as revealed in the transition from thermal to coherent statistics of the emitted light.