  We extend the model of King et al. (2004) for variability in black hole
accretion discs, by taking proper account of the thermal properties of the
disc. Because the degree of variability in the King et al. (2004) model depends
sensitively on the ratio of disc thickness to radius, H/R, it is important to
follow the time-dependence of the local disc structure as the variability
proceeds. In common with previous authors, we develop a one-zone model for the
local disc structure. We agree that radial heat advection plays an important
role in determining the inner disc structure, and also find limit-cycle
behaviour. When the stochastic magnetic dynamo model of King et al. (2004) is
added to these models, we find similar variability behaviour to before.
  We are now better placed to put physical constraints on model parameters. In
particular, we find that in order to be consistent with the low degree of
variability seen in the thermal disc component of black hole binaries, we need
to limit the energy density of the poloidal field that can be produced by local
dynamo cells in the disc to less than a few percent of the energy density of
the dynamo field within the disc itself.
