AbstractIn 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.