  We revisit our original papers on the burst mode of accretion by
incorporating a detailed energy balance equation into a thin-disk model for the
formation and evolution of circumstellar disks around low-mass protostars.Our
model includes the effect of radiative cooling, viscous and shock heating, and
heating due to stellar and background irradiation. Following the collapse from
the prestellar phase allows us to model the early embedded phase of disk
formation and evolution. During this time, the disk is susceptible to
fragmentation, depending upon the properties of the initial prestellar core.
Globally, we find that higher initial core angular momentum and mass content
favors more fragmentation, but higher levels of background radiation can
moderate the tendency to fragment. A higher rate of mass infall onto the disk
than that onto the star is a necessary but not sufficient condition for disk
fragmentation. More locally, both the Toomre Q-parameter needs to be below a
critical value _and_ the local cooling time needs to be shorter than a few
times the local dynamical time. Fragments that form during the early embedded
phase tend to be driven into the inner disk regions, and likely trigger mass
accretion and luminosity bursts that are similar in magnitude to
FU-Orionis-type or EX-Lupi-like events. Disk accretion is shown to be an
intrinsically variable process, thanks to disk fragmentation, nonaxisymmetric
structure, and the effect of gravitational torques. The additional effect of a
generic \alpha-type viscosity acts to reduce burst frequency and accretion
variability, and is likely to not be viable for values of \alpha significantly
greater than 0.01.
