[en] Cooling of a heavy particle beam in accompanying electron flow, ''frozen'' by a longitudinal magnetic field is considered. Velocity distribution of electrons is considered as abruptly flattened in the longitudinal direction (Δ sub(e long) < < Δ sub(e tr)). Under these conditions the region with Δ sub(i) < Δ sub(e tr) (Δ sub(i) - ion velocity spread) effective electron temperature is determined only by longitudinal velocity spread owing to the long-range character of the Coulomb forces and magnetization of the transverse electron motion. Here, in comparison with the Δ sub(e long) approximately Δ sub(e tr) situation the cooling rate increases sharply and ion temperature can decrease up to longitudinal electron temperature. It is shown, that under certain conditions the above effect is restricted by deflections of lines of magnetic force from the direction of a closed orbital of heavy particles at the cooling region