This simulation is mostly based on what ''Discodermolide'' and ''Fledarmus'' explained in above comments. But as ''rasool083'' said earlier, I guess in the cooling process the nucleation starts because the solution gets supersaturated, the more the solution gets cold (about 2-5 c per hour), the more the nucleation happens.
In the cooling down phase, a lot of nucleations are formed but those nucleation that are formed at the beginning of the cooling process had enough time to grow, but those that are formed at the nearly end of the process didn't grow, so they are still so small.Now by heating-up the solution a little, the last nucleations are dissolved again but the big ones stay put. Now if the cooling phase starts again, the remnant nucleations form previous cooling phase(those that had enough time to grow), strat growing again and absorb the energy. Again at the end of this process there are some small crystals that should be dissolved by heating-up a little. This process make the crystals big.
Plz correct me if I'm wrong.