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We argue that a substantial increase in the cross section for Coulomb excitation in the region of the Double Giant Dipole Resonance should be expected from Coulomb excitation of excited states involved in the spreading of the one-phonon resonance, in a manifestation of the Brink–Axel phenomenon. This generates an additional fluctuating amplitude and a corresponding new term to be added incoherently to the usual cross section. The appropriate extension of an applicable reaction calculation is considered in order to estimate this effect.