Time-dependent radiative heat flux after the beginning of thermal radiation

We develop a theoretical formalism for time-dependent radiative heat flux from one object to another in the case where the former starts radiating at a certain time. The time dependence is demonstrated for the heat flux between two isolated nanoparticles. After one particle starts radiating, the emitted energy first reaches the other one with a delay according to electromagnetic retardation, and afterwards the flux exhibits oscillatory exponential relaxation to its stationary value. For the room- or higher-temperature radiation, the oscillation period and relaxation time are determined by the resonance frequency and damping rate of the particle polarizability, respectively, being equal to dozens of femtoseconds and one picosecond for silicon carbide particles. At cryogenic temperatures, the relaxation time depends on the thermal wavelength.