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

https://blogfreely.net/borianyvyf/why-a-thermostat-problem-may-not-be-the-thermostat-at-all-4fqn

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.