We have investigated the quality factors of silicon-based photonic crystal nanocavities using the photoluminescence of a single layer of Ge/Si self-assembled islands as an internal source. We focus on membrane-type L3 elongated cavities with or without their lateral edge air holes shifted in position. The photoluminescence measurements are performed at room temperature. We show that the quality factor of the fundamental mode observed at a normalized frequency u = a/lambda~_ 0.25 is strongly dependent on the incident pump power. This dependence is associated with the free-carrier absorption of the photogenerated carriers. The slope of the quality factor vs. incident pump power gives access to the carrier recombination dynamics in these Si-based nanocavities. The measurements indicate that the carrier dynamics is controlled by nonradiative recombination associated with surface recombinations. A surface recombination velocity of 4.8 x 10(4) cm/s is deduced from the experiments. The spectral red-shift of the cavity modes as a function of incident pump power is correlated to the temperature rise due to thermo-optic effects. The measured temperature rise, which can reach 190 K, is correlated to the value estimated by a thermal analysis.