Looking for the right thermostat- is it this hard
These are very common, any thermostat that you can find that offers and &quot;Auto&quot; mode should be able to cool and heat based on what's needed without any action from your part.
However, the way you described the functionality is a bit different than what the thermostat will do. The auto feature will run a HEAT program along with a COOL program but they cannot be set to the same temperature otherwise the system will go crazy. For example, you could set the HEAT temperature to 70 and the COOL temperature to 74. Then as soon as the indoor temps goes to low 70 it would trigger the HEAT and stay around 70 until outdoor conditions are warming the house. At that point it will not activate again until the COOL set temperature is reached and will then keep it at 74.
You have to accept some variation in indoor temperature otherwise you system will just switch from HEAT to COOL all the time and you will be paying to cool down the heat that you also paid to bring into the house.