Honeywell thermostats are compatible with a wide range of HVAC systems, including Carrier heat pumps. However, it is important to check the specific model of your Carrier heat pump and compare it to the compatibility list of the Honeywell thermostat you are considering purchasing to ensure compatibility. Some of the Honeywell thermostats have compatibility with specific types of HVAC systems, such as Honeywell TH9320WF5003 Wi-Fi 9000 Color Touchscreen Thermostat, that is compatible with heat pumps with auxiliary heat.
Also, it is highly recommended that you consult with a licensed HVAC professional to confirm compatibility and assist with the installation of the thermostat. This professional can help ensure that the thermostat is set up correctly and that it is properly communicating with your Carrier heat pump.