Ok, here is my question.  How does keeping the temperature in your home lower your energy bill?  Here is why I ask.
~I got new windows in the spring. good, much better, insulation.  but keeping my temperature low has never been a strong point of mine; I like being able to be comfortable almost naked (if not so) in my house always.
~ So, assuming that there are no random energy leaks in a house (such as doors left open to the outside for hours, or wind gusts inside some how) the energy loss in the house should remain constant; for example, say 1 degree an hour.
~So, with the previous assumption unnegated, how does keeping the temperature lower help?  the energy used after, say, 2 hours of operation (a drop of 2 degrees) should be the same whether its from 68-70  or if it is 76-78.  the only difference would be if you have a regulating thermostat that drops the temperature when you are not there, in which case the energy expended would be more to raise the temperature back up.  if its simple caloric calculations (I have radiant heat, so it literally is the energy to raise a given amount of water by a given amount of heat)  then what am I missing when I hear that I should keep the temperature lower in the winter?! Why is this not making sense to me, someone help me out here!

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Your house temperature will not drop inexorably to absolute zero, rather it will tend toward the external temperature at a speed that diminishes as the difference between inside and outside approaches zero - equilibrium.

The nearer you are prepared to keep the internal temperature to the external temperature, then the smaller and slower will be the heat transfer through your walls, windows, roof and floor. In the limit, if your house was the same temperature inside and out then your heating bill would be zero.

Obviously this works in both directions, you might want your house hotter than the outside in the winter and colder than outside in the summer.

Clearly you don't want to do this so your cheapest bet is to insulate (as you have done) and slow the rate heat transfers though your walls.

If you had perfect insulation then once you'd got your house to the right temperature then you could turn of your heating/AC forever.

A little rambling - but does that help?
it does, although i'd contest the last point citing the second law of thermodynamics maybe? lol enclosed systems dissolve into entropy~ that aside of course that is a different way for me to examine the issue; although, when i think about it, it still seems the same in a sense, because the external temperature does not rise to meet the internal temperature as it drops. I think that i'm still questioning the explanation.... so what you're saying is that if my house was 100 degrees inside, the temperature would drop much faster than if it were only 70? I'm not sure how the heat exchange is accelerated due to increase in temperature
i guess that does make sense, as when we are outside, the colder it is the quicker we freeze~ the acceleration of heat transfer. although i guess where my real question would come in is if the heat is transferring through a medium, ie glass of the window, is there a set transfer cap, or will that transfer increase exponentially the wider the difference between temperatures. I appreciate your response, and hope my constant questioning isn't grating (it is, of course, how I ended up here on the atheist nexus lol)
HAHA! I got you, It must be GOD in the gaps of energy transfer!
well john d i appreciate your willingness to engage in my question, and for that, i will friend you. (sometimes i think my 3 year old knows more than i do, kids these days eeeesh)
You bunch of egg heads! I was all muddled reading this... the replies gave me that "ah ha" moment. Ugh... I need caffeine!
Give a man fire and he'll be warm all night.

Set a man on fire and he'll be warm for the rest of his life.
it's the bulbs
Hi, I think this has been answered pretty well but a few thoughts that may help. Keep in mind that thermal energy is not equal to temperature. The amount of energy needed to change the temperature of a system by 1 degree c is the Heat capacity of the system. energy added = Heat Capacity * delta temp or
dQ = C * dt . Now back to your house. The heat flow out of you house depends on the difference in temp between the inside and outside ( T in - T out) call it DT. This is the thermal potential think of it like a Voltage in a simple dc circuit ( if that helps ) , now of course it also depends on how easy it is for the heat to flow or the thermal resistance ( how good your windows are) So now the Heat Loss form your house can be modeled as dQ/dtime = ( T in - Tout ) / R where R is the total thermal resistance between the inside and outside of your house. So this is just another way of saying that Watts of power lost by your house to the environment is directly proportional to the temperature difference and inversely proportional to how well insulated it is.
But since the title of your post was help with critical thinking don't take my word for it think about how you would do an experiment to test it.
Right, I have a pretty good understanding of that~ I guess where my question comes in is " is there a difference in the time that heat is lost from I(nside) Temp = O(utside) Temp/ if it is 32* outside, constant, is the rate of heat loss inside steady between 100* to 75* as opposed to 75* to 50* (both drop 25*, would it be in the same amount of time? Is heat loss a constant proportion, or merely proportional to the ratio of I temp to O temp [ Or put another way, does heat transfer through a solid medium increase with the disparity of opposing temps, or is there a heat-loss cap, so to speak, where a maximum of energy is transfered, thus leveling out the loss of energy to a point where it makes no difference in time]
So your question is if out side temp is constant 32, is the heat flow rate from inside to outside greater if the inside temp is 100 then it is if the inside temp is 75. Id say yes. If you heat your house up to 100 f when its a constant 32 outside then turn off the heat and time how long it takes to drop to 75 then time how long it takes to drop to 50 you will get a significantly longer time for the second.
in fact the time to drop the last degree from 33 to 32 would be very long. This does require solving a differential equation to calculate the time, but if you take the case where both inside and outside temps are constant its pretty easy to calculate the steady state energy flow from inside to outside (assuming we know the thermal resistance which of course we dont). And since energy is conserved to keep the inside temp constant that's how much heat / per unit time your furnace must be generating (average power).

Is there a cap where the heat flow saturates and increasing the internal temp does not lead to a higher rate of loss. I don't think so for any practical case. We could imagine some hypothetical material whose thermal resistance increased with temperature, so your walls and or windows insulated better when it was hot inside that would tend to flatten out the curve.

If you enjoy thinking about this you might want to take some physics or thermo dynamics courses.
Take Care
So then If graphed, the heat exchange should resemble a parabola, with the tail tapering off as temperature equality is near... hm, I wonder, imagining a parabola of that sort, whether it would ever actually cross the axis, since transfer becomes slower the closer the temperatures are, if there is a point where, say, 32.001111 will never reach 32.00000000 because of the decrease in transfer. I'm just speculating here, but it seems interesting to me LOl thanks for your help in this matter. I have radiant heat in my house, fueled by natural gas, so I'm trying to see if I can get away with heating my house to 76* because I like it hot LOL

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