This is probably the most difficult part of the process. It is not so much a technical challenge (although this step is technical in nature) but more of a test of your patience. It may feel like forever before you bring the temperature down to where you can remove the piece from the kiln. Properly heating and cooling a casted glass object is essential to its stability. If not done properly the internal stresses of the glass will be locked in place as it cools making it very likely to fracture or explode.
This is the molten glass after it had melted into the plaster casting mold. The photo was taken at around 1000 degrees (approaching the annealing temperature)
The process to properly cool a warm glass object is called annealing. It is a process by which you maintain a constant temperature of the glass object at a point where it is still soft enough to "adjust" the molecular alignment of the silica atoms into a state that minimizes internal stress. Once you drop below the annealing temperature the alignment of molecules becomes rigid and any stresses are locked in to the amorphous solid. Being an amorphous solid, glass does not have a clear state transition between solid and liquid states but rather changes in viscosity across temperatures. It is not a liquid in solid state as it is commonly thought of, and no, stained glass windows from ancient cathedrals are not flowing down from the force of gravity. The thickening of the glass that is observed is a result of the manufacturing process of glass from that era and an understanding that thicker glass on the bottom was more stable than thicker glass on the top.