We present a systematic study of the Giant Dipole Resonance (GDR) at high temperatures (T>4 MeV) in the framework of a semiclassical approximation that uses the ml and m3 RPA sum rules to estimate the GDR mean energy. We focus on the evolution with T of the collective nature of the GDR and of the L= 0, 2, 3 and 4 isoscalar resonances. We find that the GDR remains particularly collective at high T, suggesting that it might be possible to observe it experimentally even at temperatures close to the maximum one a nucleus can sustain.