The evolution of ablative Rayleigh–Taylor instability (ARTI) induced by single-mode stationary and time-varying perturbations in heat flux is studied numerically in two dimensions. Compared with the stationary case, time-varying heat-flux perturbation mitigates ARTI growth because of the enhanced thermal smoothing induced by the wave-like traveling heat flux. A resonance is found to form when the phase velocity of the heat-flux perturbation matches the average sound speed in the ablation region. In the resonant regime, the coherent density and temperature fluctuations enhance the electron thermal conduction in the ablation region and lead to larger ablation pressure and effective acceleration, which consequently yield higher linear growth rate and saturated bubble velocity. The enhanced effective acceleration offers increased implosion velocity but can also compromise the integrity of inertial confinement fusion shells by causing faster ARTI growth.