Classical molecular dynamics simulations are performed to demonstrate a possible mechanism for nonstatistical energy partitioning in desorption processes initiated by rapid surface heating. The model is a diatomic desorbed from a cold cluster of 19 Pt atoms upon a rapid increase in the cluster temperature. Physisorbed systems display vibrational energy product distributions indicative of energy flow mediated by the weak bond. Specifically, chemically bound diatomic molecules are desorbed vibrationally cold, due to inefficient vibrational energy flow between the physisorbed motion and the internal molecular vibration. On the other hand, for van der Waals bound diatomics ready energy flow is observed indicating that with establishment of an approximate frequency match between the physisorption mode and the internal vibration no bottleneck to energy transfer is evident. In general, the desorption process starting from a cold surface is indirect. Trajectories migrate along the surface resulting in effective translation-rotation coupling and broad rotational distribution of the products. For chemisorbed systems, the surface-absorbate mode does not influence strongly the nature of vibrational excitation in the internal mode of the admolecule, but rather direct interaction with the surface motions plays the primary role in any energy transfer. The systems studied exhibit a wide range of behaviors, from RRK-like, where energy is nearly equipartitioned, to highly selective, where the internal vibration of the admolecule is completely isolated due to the existence of bottlenecks. The mechanism which gives rise to these observations is discussed and the particular role of fluctuations, or impulsive interactions, is highlighted.