Log homes are not built like most other types of homes or buildings. In fact, by definition log homes have solid exterior walls with some solid interior walls, too. So when it comes to installing central air conditioning, there is often very limited space for ductwork, returns, and other mechanical necessities. The problem gets more complicated when the home design has an open floor plan and even fewer walls.
Read more about the log home case study here: A Cool Log Home In The Woods