  In this article, we proceed to study convection as a possible factor of
episodic accretion in protoplanetary disks. Within the model presented in
Article~I, the accretion history is analyzed at different rates and areas of
matter inflow from the envelope onto the disk. It is shown that the burst-like
regime occurs in a wide range of parameters. The long-term evolution of the
disk is also modeled, including the decreasing-with-time matter inflow from the
envelope. It is demonstrated that the disk becomes convectively unstable and
maintains burst-like accretion onto the star for several million years.
Meanwhile, the instability expands to an area of several tens of astronomical
units and gradually decreases with time. It is also shown that at early stages
in the disk evolution, conditions arise for gravitational instability in the
outer parts of the disk and for dust evaporation in the convectively unstable
inner regions. The general conclusion of the study is that convection can serve
as one of the mechanisms of episodic accretion in protostellar disks, but this
conclusion needs to be verified using more consistent hydrodynamic models.
