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We give an exact solution of the $5D$ Einstein equations which in 4D can beinterpreted as a spherically symmetric dissipative distribution of matter, withheat flux, whose effective density and pressure are nonstatic, nonuniform, andsatisfy the equation of state of radiation. The matter satisfies the usualenergy and thermodynamic conditions. The energy density and temperature arerelated by the Stefan-Boltzmann law. The solution admits a homothetic Killingvector in $5D$, which induces the existence of self-similar symmetry in 4D,where the line element as well as the dimensionless matter quantities areinvariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.

AN EXACT SELF-SIMILAR SOLUTION FOR AN EXPANDING BALL OF RADIATION