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Here is my situation: I am a Chicagoan living in Prague. The apartment building I live in is charging OUTRAGEOUS amounts of money above and beyond the normal amount we pay for utilities.

I would like to mathematically prove that what they are charging is not possible.

Prague has a temperate climate. It rarely snows here. Winter is much, much milder than in Chicago. I checked average temperature for January, and it shows a typical high of 34C, and low of 25C. Hence, the amount of heat needed should be considerably less than what you'd expect in Chicago where you have truly sub-zero temperatures.

Here is the scenario: I have a 160 square meter apartment. That's really four main rooms (kitchen, living room, and two bedrooms). There is a radiator in each room. Very often, I have them TURNED OFF because it's just so naturally hot in this building. Europeans don't seem to have any concept of how hot it is, and they still wear sweaters while I'm broiling in just a short sleeve shirt. So as you can see, I don't consume much myself.

I live on the fourth floor of a five story building. This is an old building, so walls are thick. Heat stays in (just as it is naturally cool in summer; no air conditioning). The windows are actually two complete sets of windows, so heat does not escape, and noise doesn't bother you.

I was charged the equivalent of $650 for each month of what I consider "winter" here, December-March. These are the only months one could even believe that "extra" needs to be charged for heating. I even dispute it is that long of a winter, but for the sake of argument let's say four months of "real" winter.

I was charged the equivalent of $2,600 extra, on top of normal utilities. The building is charging other people similarly outrageous amounts, based on the relative size of their apartment. Several people hired lawyers and tried to get the local government to do an official check, but they are ineffectual.

Can you create an estimate of how much energy it should take to heat an apartment like mine? I realize there are so many variables, so just create a scenario you feel is reasonable. I like to keep the apartment cool, and even with the radiators closed have had to open windows just to reduce the temperature. (these Czechs waste heat like mad; if MY apartment is too hot with closed radiators, theirs are broiling).

Once again, I realize there are too many variables, but please just construct a likely scenario. Prague is nowhere near as cold as Chicago, and I'm being charged more to heat an apartment than for my entire four-bedroom house in Chicago. I think it's a scam, and I want to be able to prove it mathematically.
I do believe the company that owns this building simply takes ALL their costs (insurance, depreciation, etc.) and divides them up among tenants and then creates bills to cover all their expenses, not just we should be liable for. Or maybe they decide how much they want to make each year, and then concoct bills to fit that scenario.