Motivated by the Laser-Induced Incandescence (LII) technique for in situ sizing of submicron aerosols, non-continuum heat transfer between an isolated, motionless, highly overheated spherical particle and its cooler surrounding gas is studied using the Direct Monte Carlo Simulation (DSMC) technique for the ＇calibration＇ case of a monatomic, hard-sphere gas. We find that our numerical DSMC results are adequately described by a variable property extension of Fuchs＇ two-layer theory, whereas other interpolation formulae fail in the Knudsen transition regime when the particle/gas temperature ratio is large. On this basis, tractable equations are provided which will permit accurate estimates of the transition regime heat transfer coefficient for a polyatomic ideal gas with arbitrary temperature-dependent heat capacity and Fourier conductivity.