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

https://lukasgzfi082.opalvector.com/posts/how-to-cool-a-salt-lake-city-home-that-has-no-ductwork

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.