  We analyse disc heating and radial migration in N-body models of growing disc
galaxies with thick and thin discs. Similar to thin-disc-only models, galaxies
with appropriate non-axisymmetric structures reproduce observational
constraints on radial disc heating in and migration to the Solar Neighbourhood
(Snhd). The presence of thick discs can suppress non-axisymmetries and thus
higher baryonic-to-dark matter fractions are required than in models that only
have a thin disc. Models that are baryon-dominated to roughly the Solar radius
R_0 are favoured, in agreement with data for the Milky Way. For inside-out
growing discs, today's thick-disc stars at R_0 are dominated by outwards
migrators. Whether outwards migrators are vertically hotter than non-migrators
depends on the radial gradient of the thick disc vertical velocity dispersion.
There is an effective upper boundary in angular momentum that thick disc stars
born in the centre of a galaxy can reach by migration, which explains the
fading of the high-alpha sequence outside R_0. Our models compare well to Snhd
kinematics from RAVE-TGAS. For such comparisons it is important to take into
account the azimuthal variation of kinematics at R ~ R_0 and biases from survey
selection functions. The vertical heating of thin disc stars by giant molecular
clouds is only mildly affected by the presence of thick discs. Our models
predict higher vertical velocity dispersions for the oldest stars than found in
the Snhd age-velocity dispersion relation, possibly because of measurement
uncertainties or an underestimation of the number of old cold stars in our
models.
