Migrators’ contribution to the disc heating. First row: radial profiles of the vertical velocity dispersion, σ_z(r), for non-migrators (dashed black curve), outward going migrators (solid brown curve), and inward migrators (dash-dotted green curve) for the gSb model, estimated in the time periods indicated in the top row of each column. Second row: σ_z(r) estimated for non-migrators (dashed black curve), all migrators (i.e., inward and outward going, solid green curve), and the total population (dashed-dotted blue curve). Third and Fourth rows: same as the first and second rows, respectively, but for the radial velocity dispersion profile σ_r(r). An unexpected result is that outward migrators cool the disc inside the bar’s OLR (and inward ones heat it), unlike in the case of σ_z. Some increase in σ_z and σ_r from migrators is seen beyond the OLR, while the inner disc is cooled both radially and vertically. Figure 6 quantifies better the migrators’ contribution to σ_z and σ_r.