What is the most efficient temperature to keep your house at? I live in the north east of the USA. I am wondering if there is any information as to what the most efficient temperature to keep your house at. I have oil burning forced hot air with an efficient burner
 A: 
I live in the north east of the USA. I am wondering if there is any information as to what the most efficient temperature to keep your house at. I have oil burning forced hot air with an efficient burner

The most efficient heating at any temperature occurs at thermal equilibrium or heat balance where the rate of heat lost is equal to the rate of heat produced. This is the function of a thermostat and many are tailored for different applications (oil heat vs electric) but they all essentially regulate the amount of heat generatated. The better the thermostat, the more efficiently the regulation will occur while maintaining the set temperature. Those that are programmable are very useful. Adding or improving existing insulation will reduce the rate of heat loss and consequently reduce the rate of heat production and lower your bill.
So, get a good thermostat and insulate for the best results.
A: Efficiency is one of the things you might care about, but not necessarily the only thing. Efficiency is the fraction of energy you use that actually goes toward the goal you have. If you run a machine, some energy goes toward doing work, and some goes to overcoming friction and heating things up. That part is wasted. Ideally you want $100$% of the input energy to go into doing work.
When you heat your house with oil, you start with the energy in the oil. You burn it and use the heat to heat your house. But some of that heat goes into warm exhaust instead of your house. So not $100$% efficient.
If you use electricity, it depends on how you measure it. Electricity arrives at your house. All of it is turned into heat and warms your house. Sounds like $100$%. But usually that electricity is generated with fuel. A lot of the energy in the fuel goes into heating exhaust at the power plant. More gets lost in the resistance of the wires leading to your house.
But you might also want to consider the price of electricity vs the price of fuel. If oil is cheap, it might come out cheaper to use oil than electricity regardless of efficiency.
If you live next to a forest, burning wood in a stove might be free. But it is a lot of work to cut wood, haul it to your house, etc.
What temperature to use is something like this. A high temperature is more comfortable. But it uses more energy. If you are using oil or electricity, it uses more money. If you are using wood, it takes more work. This is true regardless of efficiency.
A better approach would be a merit function. This is a function you figure out based on your personal preferences. You decide how painful it is to be cold. You assign a number that represents the degree of pain to each temperature. Since you are using oil, you also decide on a number that represents how painful it is to pay for oil at each temperature. You add these pains together to get a merit function. It is up to you how to assign the numbers. If you don't have much money, you might assign big pain numbers to that. If you like your comfort, that might have the bigger number.
Then you look for the temperature with the least pain.
This also helps you compare different methods of heating your house. It might be easy to choose between oil and electricity simply based on price. But oil vs wood is harder. For that, you come up with a second merit function for wood. You use the same pain numbers for comfort. But you come up with new numbers that represent how painful it is to chop wood and haul it around. Then you compare the two functions and see which choice is the least painful.
