Interesting question and bit complicated.
Take a look at http://www.engineeringtoolbox.com/air-specific-heat-capacity-d_705.html
For dry air at sea level, it takes about 1 kJ to heat 1 kg of air one degree Celcius.
- Based on the energy source (electric, oil, gas) you can find the cost per kJ. Convert watts to joules and google the efficiency of the type of heating system. ( X $/kJ)
- To find the kg per minute of air that leaves the door, you might try this... Sprinkle some confetti from above the door frame. The angle at which the confetti falls tells you about the speed of the stream of air leaving the door and from that, the kg of air per day. ( Y kg/day)
- Finally, how much warmer do you want the air? ( Z degC)
Now you can write...
$/day = (1kJ/kg.K) * ( X $/kJ) * ( Y kg/day) * (Z degC)
Expect a lot of error. Think about what would be a reasonable number, it might be anywhere from 5?o 50?f the daily heating bill. Are the original assumptions good? Is the air really dry? Is the building used for warehouse, factory, office? Does the work generate "waste" heat? Can you check it out at night or on the weekend?
Also, think about the positive reasons for having th door open. Does the building need the ventilation? Are there odors or high humidity? Is there forced air heating or radient heat? Do the employees complain about health issues related to ventilation at the end of the day? Possible longer term health issues? Can you take a customer survey? Will the product suffer?
At the end of the day the easiest and most accurate way to know is, just do it. Take careful records several times a day for the week before, a week during a trial and a week after.
Finally, about the supervisors, if they are like some of the supers I've had, you don't want to confuse them with facts and details. Can you make it look like their idea so that they get the credit and you get the blame? Ultimately, it's their job, their responsibility.
You want to "confront" the bosses? Careful, the next day you might be confronting the unemployment line. Good luck!