...And how to cool a large building efficiently.

Consider geothermal cooling as an answer.

Castles can be big, no doubt about it. You shouldn't have to be a Vanderbilt to afford one, or the associated costs of keeping the interior at a comfortable temperature. Some people choose to build their own castle themselves due to the prohibitive cost of having someone build it for them. $100,000 of materials and a lot of DIY will build you a pretty darn big castle, $100,000 and a contractor would be lucky to get you a very small cottage in most places. So DIY castle builders generally don't have a lot of spare cash to throw around to begin with, otherwise they'd have someone build the castle for them at $500,000 and not be a DIY builder!

At any rate, all that square footage requires some form of climate control that could be prohibitively expensive to operate in that volume. One of the benefits of a castle that is built from stone or cement is the thickness of the walls and material type can retain the coolness of the night and prevent the heat of the sun from warming the interior of the building too much during the day. Planting trees to shade the building is an excellent way to provide cooling; trees act as natural air-conditioners, and when planted strategically, prevent some sunlight from reaching the building and heating it in the first place.

Then there's geothermal cooling (Examples and Explanation). Basically what this system does is use the Earth itself as a heat sink. I'm sure many have heard that the Earth maintains a relatively constant temperature (45-55 degrees F), and this is what the system takes advantage of. It consists of running a tube for a fluid (such as water or an anti-freeze solution) into the Earth either in a "well" or some kind of pattern, allowing the earth to soak up the heat in the fluid, which then loops the cooled liquid back into the building through a heat exchanger which takes the heat in the air and transfers it to the fluid, and back out the fluid goes. The warm air in the house is passed through the heat exchanger and cooled, and then directly back into the house, or on into a conventional air-conditioning system. In a conventional A/C system, the pre-cooled air means the system doesn't have to run as hard or as long to cool the ambient air in the building to a comfortable level.

It isn't cheap to install this type of system, as it requires quite a bit of excavation or drilling into the earth. A builder would have to take into consideration the current and future expected energy costs of cooling the building using geothermal vs. conventional methods, along with the immediate costs of installing the system. The efficiency of the system along with low maintenance due to simplicity, low operating costs, environmental benefit of not needing Freon or comparable coolant, and it could be comparable or considerably less in total cost to a conventional system in the long run.