If the thermostat is on the first floor in the center room and you're only concerned about the temperature in your room, opening your windows can still affect your heat bill, even if you isolate the change in temperature to your room. The reason for this is how the heating system operates and distributes heat throughout the house.
When you open the windows in your room, even if you isolate the temperature change, the heat loss from your room will be significant. The heat produced by your heating system is intended to warm up the entire house, not just one room. When you open the windows, the warm air will escape, and cold air from the outside will rush in, causing your heating system to work harder to maintain the desired temperature on the first floor.
Here's what happens in this scenario:
Heat Loss: When you open the windows, the warm air in your room will escape, and cold air from outside will come in to replace it. This leads to heat loss from your room.
Temperature Difference: With cold air coming into your room, the temperature in your room will drop below the set thermostat temperature on the first floor.
Heating System Response: Since the thermostat is on the first floor, it will sense the temperature drop in the center room and trigger the heating system to turn on or work harder to bring the temperature back up to the set point.
Increased Energy Consumption: The heating system will need to use more energy to compensate for the heat loss caused by the open windows. As a result, your heat bill will likely increase.
To save on your heat bill and ensure efficient heating, it's better to keep the windows closed while your heating system is running. If you want to control the temperature in your room separately, consider using a space heater or adjusting the vents in your room to regulate the airflow and direct more heat there. However, be sure to follow safety guidelines when using space heaters.