We study the excitonic recombination dynamics in an ensemble of (9,4) semiconducting single-wall carbon nanotubes by high-sensitivity time-resolved photoluminescence experiments. Measurements from cryogenic to room temperature allow us to identify two main contributions to the recombination dynamics. The initial fast decay is temperature independent and is attributed to the presence of small residual bundles that create external nonradiative relaxation channels. The slow component shows a strong temperature dependence and is dominated by nonradiative processes down to 40 K. We propose a quantitative phenomenological modeling of the variations of the integrated photoluminescence intensity over the whole temperature range. We show that the luminescence properties of carbon nanotubes at room temperature are not affected by the dark/bright excitonic state coupling.