Heat transfer by thermal radiation from a hot spherical particle to ambient water through the concentric vapor shell is analyzed by the use of different theoretical models. In the case of the vapor layer thickness Delta comparable with the radiation wavelength, the wave effects are taken into account. For greater values of Delta, the problem solution is derived by combination of the Mie theory for the particle emissivity, the Fresnel's equations for radiation reflection/refraction on the vapor-water interface, and the radiation transfer equation for calculation of heat absorption profiles in water. A justified approximate description of the radiation heat transfer between cerium melt particles and boiling water, as applied to vapor explosion analysis in the case of nuclear reactor severe accident, is proposed. Numerical examples illustrate effects of the particle size and the vapor shell thickness.