A passively mode-locked Nd:YAG oscillator operating in TEM00mode is investigated theoretically and experimentally. It is shown that a mode-locking threshold well above the normal lasing threshold exists and that this second threshold is of a probabilistic nature. This means that mode locking at a given pump rate in the region of threshold occurs only with a certain probability due to the Gaussian statistics of spontaneous emission. Experiments agree qualitatively with theory. Furthermore, thermal effects in the liquid absorber are shown to play an important role in mode-locking systems; they introduce an additional time-dependent loss or gain, depending on the experimental setup. This can either lead to increase of mode-locking threshold or to the appearance of higher order transverse modes and possible damage of laser components.