Yep. Whatever the temperature, underground is more thermally stable and insulated from the seasonal temperature swings experienced above ground. Additionally, it would be unnecessary to design the structure to withstand potentially high hurricane wind forces. The structure would also likely require a less massive foundation to support the weight. Trusswork could transfer the weight-load latterally against the solid bedrock as one continued to dig downward.
How much bedrock is down there? Seems like a daunting task to tunnel through bedrock if it goes down a ways.