High-power femtosecond laser radiation propagates nonlinearly in air, exhibiting pulse self-focusing and strong multiphoton medium ionization, which leads to the spatial fragmentation of laser pulses into highly localized light channels commonly called filaments. Filaments are characterized by high optical intensity and reduced (even zero) angular spreading and can contain laser plasma or be plasmaless (postfilaments). The presence of optical turbulence on the propagation path dramatically changes pulse filamentation dynamics and in some cases causes pulse fragmentation enhancement and collapse arrest. For the first time, to the best of our knowledge, we experimentally and theoretically investigate the transverse profile of Ti:sapphire femtosecond laser radiation nonlinearly propagating a 65 m air path to the region of postfilament evolution after passing through an artificial localized air turbulence. We show that when a turbulence layer is placed before the filamentation region, the average number of high-intensity local fluence maxima (“hot points”) in the beam profile and their sizes grow as the turbulence strength increases, and then saturates at some levels. On the contrary, the deposition of a turbulence screen within the filamentation region has almost no effect on either the number or the average diameter of postfilaments.