My heat pump blower is on continuously and blows cold air into the room even if the thermostat is on heat and even if the thermostat's temperature is set higher than the target temperature.

I am no expert. However, our home just had the same problem with it's unit. I paid for the Heat and Air pro's 75 dollars to just do a service call.

My news was not good. I was hopeing that it needed freon which may be the case.
Only it was not. It is the Compressor. 1,700 for a repair, I do not have, for it to run awhile and break again, or 8,000 for a new system.

vpsi, what temp is it outside? Do you have an emergency heat setting on your thermostat? If you do, flick that on and let us know if warm air comes out

Brand?

Exact model number?

Will the thermostat reach its target temp or is it losing ground? More info will help.