How thermal energy is transferred by radiation?

Radiation is the transfer of energy by electromagnetic waves.

Considering the dual nature of electromagnetic radiation, you could also consider it to be transferred by photons of the electromagnetic radiation.

The rate of transfer of radiation is given by the surface area of the radiation source, the surface area of the object receiving the radiation, a geometric coefficient accounting for how much of the radiation from the source actually hits the receiving object, a physical constant called the Stephan-Boltzman constant, the reflectivity, transparency, and absorbtivity of the receiving object for the wavelengths of the radiated energy, and the difference in the 4th power of the thermodynamic temperatures of the objects.