Opening the windows in your room while isolating the change in temperature to that specific area would not directly impact your heating bill. However, there are a few factors to consider that could indirectly affect your overall heating costs.
Heat Loss: When you open the windows, even if it's just in one room, there will be some heat loss to the outside. This means that your heating system will have to work harder to maintain the desired temperature in your home. If your heating system runs longer or more frequently due to the heat loss, it could lead to increased energy consumption and higher heating bills.
Thermostat Placement: You mentioned that the thermostat is located on the first floor in the center room. Opening windows in your room while keeping the temperature isolated could potentially create a temperature imbalance. If the temperature in your room drops significantly compared to the rest of the house, the thermostat might continue to call for heat, assuming the entire house is not adequately heated. This could result in your heating system running longer than necessary and potentially increasing your heating bills.
Air Infiltration: Opening windows can introduce cold outside air into your room. Even if you isolate the temperature change, the colder air entering the room may impact the overall comfort level. To compensate for the cold air infiltration, you might be inclined to increase the thermostat setting, which would, in turn, increase your heating costs.
In summary, while opening your windows in one room and isolating the temperature change may not directly impact your heating bill, it could indirectly affect your energy consumption and costs. It's important to consider heat loss, thermostat placement, and potential air infiltration when making decisions that can impact the heating efficiency and comfort of your home.