For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option

https://westus1.blob.core.windows.net/home-blogger/why-your-mini-split-stops-cooling-in-july.html

For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option, especially where existing heating is radiant, hydronic, or space-heater based.