We are here concerned with experiments in which time-of-flight (TOF) measurements are made with particles which are vaporized, sputtered, or desorbed due to a pulsed heat source. If the emitted particle number density is low enough, the particles will disperse collisionlessly. Provided the emission is truly thermal, the velocities will then be described by a "half-range" Maxwellian, i.e. a Maxwellian with only positive velocities normal to the target, for which it is well known that the surface temperature, Ts, and the energy, Ê, defined by the peak position of the TOF spectrum are related by kT s = Ê/2 . More commonly the emitted particle density is high enough that near-surface collisions occur. For as few as 3 collisions per particle a Knudsen layer forms, i.e. there is a layer within a few mean free paths of the target surface in which the distribution function evolves to a "full-range" Maxwellian in a center-of-mass coordinate system. We show that for on-axis measurements the relation kT s = Ê/2 is replaced by kT s = Ê/η K, with η K ranging from 2.52 for a monatomic species to 3.28 for a species with many accessible internal degrees of freedom. Failure to recognize the formation of a Knudsen layer thus leads to a severely overestimated value for Ts, at least for an-axis measurements.