Well Sir, that’s a somewhat complex question. I assume you know this, already, and indeed you mention one of the complications later, i.e. “ambient temp.” There are other factors that must be controlled for.
It appears that you are angling toward a conclusion that amounts to, “Since this stuff is complex, we should just ignore the science - it’s all a bunch of nonsense.” History is full of illuminating examples of why this thinking is wrong. In reality, it’s not necessarily “voodoo” even if we are not able to measure it, as historically with our technology not yet being apt. Humanity’s recent and ongoing work with the Higgs Boson is a good illustration of this.
To a very high degree of precision. In this case we are able to measure it. (Okay, so what does “high” mean, there? 
) As a practical matter for most of us, a small percentage of possible error will be okay, i.e. in our considerations of calories, if we are off by 2% or 3%, it’s not going to be a big deal. If total calories are 2500, then we’re talking about 50 - 75 calories, eh?
So, hook the person up to a good indirect calorimeter, and have at it. The best ones have less than 1% error, even as low as ~0.25%. Out of that 2500 calories, we are now down to 6 - 25 calories of error.
If that is not a satisfying amount of accuracy, then let’s go with direct calorimetry - put the person inside the calorimeter. When you ask, “How many calories…” you are talking about energy over time, as with how many calories per day, per hour, etc. So, do many trials, always controlling for other variables, and get an average in the end. Very likely, we will know the figure to a fraction of a calorie.
The question itself also matters - what concept are we addressing? Human metabolism is exothermic, overall - if the subject continues living, then he’s producing substantial heat, anyway, without regard to external temperature. So, if we want to control for all other factors, to “guard out” the metabolic goings-on that proceed regardless, then we need to do series of trials at different temperatures.
This would involve maintaining the same relative humidity, diet, activity level, etc. People do (naturally) use more energy when it’s colder than normal body temperature. (And interestingly - there is a point where when it’s hot they will be using the same increased energy, i.e. they are expending energy to keep cool.)
Some work has been done on this - there’s one study about variation in body temperature and energy expenditure in response to mild cold - 9 (Dutch, I believe) guys who averaged 76 kg or 168 lbs were studied at 16° and 22°C (61-72°F). At the colder temperature they used ~5% more energy. Note that they did not maintain the exact same body temperature - they were a little colder in the colder environment. To figure the exact caloric requirement to maintain the same body temperature, their activity would have had to have been raised slightly to achieve the same temperature as at 22°C.
As above, more trials are better than fewer. And on every day, the other possible confounding influences would have to be controlled for.
Also as above, it depends on exactly what you are asking for. If we want a straight up “response to temperature” caloric solution then temperature needs to be the only variable.
Not nearly enough information is given there. The answer may be yes or no. There is a point of thermoneutrality where we are not expending any energy at all to stay warm. The bigger we are, the lesser that temperature is. A mouse, for example, uses a lot of energy, more than 1/3 of total energy, to stay warm at 22°C. For a full-grown normal or obese person, it’s not much at all at that temperature, despite it being 15-16°C less than body temperature. Does the person know what their thermoneutrality temperature is? Your question does not give that information, for example.
But of course in general the answer will essentially always be “no.”
And so what? What if I’d just said the answers to your questions are all “no”? That we are not naturally equipped to measure energy - directly, in that way - does not alter the physical and biochemical realities of life.
I’m not accusing you of being truly “anti-science.” Above, you say you don’t think the “energy balance is irrelevant.” That is a good beginning.
(You know, that bathwater that usually accompanies the baby.)
Mark, one of the most brutal examples of taking things out of context, ever. You couldn’t even make it to the end of the sentence. 
I hope things are going well for you in dear old Blighty. 
(She needs to clarify that.)
