What a lot of the nay-sayers seem to ignore is the concept of thermal mass,
With the sheer mass of rock surrounding a subterrainian DC, there is an awful lot of heat that can be absorbed. Often to the extent of weeks or months of normal heat load. (Google specific heat capacity for more information)
Due to the large area of the rocks the heat ebbs away fairly easily into deeper rocks, especially if the rocks are damp.
If this isn't enough alone to stop it long term, then sure add some aircon, but you should able to use the cool night air more than most other DCs, since the rocks soak up the 'coolth' as well as the warmth...