Context. The stellar migration of the galactic disc stars has been invoked to explain the dispersion of stellar metallicity observed in the solar neighbourhood. Aims. We seek to identify the dynamical mechanisms underlying stellar migration in an isolated galaxy disc under the influence of a bar. Our approach is to analyse the diffusion of dynamical quantities. Methods. We extend our previous work by exploring Chirikov's diffusion rate (and derived timescale) of the radial action J R in an idealised N−body simulation of an isolated disc galaxy. We limit our study to the evolution of the disc region well after the formation of the bar, in a regime of adiabatic evolution. Results. The J R diffusion timescale T D (J R) is less than 3 Gyr for roughly half the galaxy mass. It is always much shorter than the angular momentum diffusion timescale T D (L z) outside the stellar bar. In the disc, T D (J R) ∼ 1 Gyr. All non-axisymmetric morphological structures that are characteristic of resonances and waves in the disc are associated to particles with T D (J R) < 3 Gyr and T D (L z) > 10 Gyr. Short T D (J R) can be explained by the gradual de-circularisation of initially circular orbits (J R = 0) under the effect of intermittent. Inner Linblad resonance (ILR) scattering by wave trains propagating in the disc, well beyond the outer Lindblad resonance of the bar (OLR). This leads to a moderate secular heating of the disc beyond the bar's OLR for 7 Gyr, which is comparable to solar neighbourhood observations. The complex multi-wave structure, mixing permanent and intermittent modes, allows for multiple resonance overlaps.