The answer to 'why is my heat pump blowing hot air' is that your heat pump is likely in the heating mode and is working as intended. Heat pumps provide both heating and cooling by moving heat from one place to another, and when in heating mode, they will blow warm air into your home.
Some common causes for a heat pump blowing hot air include: the thermostat is set to heating mode, the outdoor temperature is below the heat pump's effective operating range, the heat pump needs maintenance or repair, or there is an issue with the refrigerant levels. If the hot air is not warming your home effectively, it's best to call an HVAC technician to diagnose and repair the issue.