Abstract Accretion onto protostars may occur in sharp bursts. Accretion bursts during the embedded phase of young protostars are probably most intense, but can only be inferred indirectly through long-wavelength observations. We perform radiative transfer calculations for young stellar objects (YSOs) formed in hydrodynamic simulations to predict the long wavelength, sub-mm and mm, flux responses to episodic accretion events, taking into account heating from the young protostar and from the interstellar radiation field. We find that the flux increase due to episodic accretion events is more prominent at sub-mm wavelengths than at mm wavelengths; e.g. a factor of ∼570 increase in the luminosity of the young protostar leads to a flux increase of a factor of 47 at 250 $μ$m but only a factor of 10 at 1.3 mm. Heating from the interstellar radiation field may reduce further the flux increase observed at longer wavelengths. We find that during FU Ori-type outbursts the bolometric temperature and luminosity may incorrectly classify a source as a more evolved YSO due to a larger fraction of the radiation of the object being emitted at shorter wavelengths.