Autoclaves can cool their loads in many ways. The important thing to remember that whilst it is important to cool the load quickly as possible, it is more important to cool the load as safely as possible.
Depending on the type of autoclave you buy, you will probably have either fan cooling or water jacket cooling. Fan cooling consists of one or more fans, which, at the appropriate stage of the cycle blows air around the outside of the chamber which dissipates the heat and cools the vessel and load. This method is inexpensive but not tremendously efficient. Water jacket cooling is far more effective at cooling the vessel and load, as the cooling medium is in direct contact with the outside of the vessel. The cost of a water jacketed autoclave however tends to be higher than that which uses fans.
The longest cycle for a lab autoclave is usually the media cycle. The cooling stage usually needs to be slow in order to prevent bottles/containers from breaking, or to prevent media volume loss due to boiling-over. If the cooling is too fast, the chamber reaches atmospheric pressure too quickly which can cause the breakage or volume loss. An increasingly popular method of speeding up the cycle times of liquid loads and reducing the above risks is to specify an air ballast system. This system basically introduces an over-pressure into the chamber during cooling using compressed air. With sealed media, this equilibrates the pressure between the chamber and the inside of the sealed bottle/container, thus preventing the breakage. With unsealed media, the over-pressure helps to keep the media inside the bottle/container.