Update 2019-07-19: there are several errors in the post below. A better calculation is at the end of my rough utility costs post.

Growing up, my parents always kept the thermostat set low to save money. Now that I'm living elsewhere, it would be nice to know how much it costs us to set the thermostat at 68F instead of 62F. What is the marginal cost of a degree (F)?

We live on the third floor of a triple decker apartment building. When we visited the apartment in February, before moving in, the apartment was empty and the heat was turned off. It was about 50F then, heated from the landlord's apartment below, so I'll use 50F as the temperature this apartment would be naturally in February.

Our gas bills over the time we've lived here have been:

Month		Cost
March	$116
April	$41
May	$22
June	$27
July	$23
August	$22
September	$25

Our gas bill represents both heat and hot water. It looks like in months where we don't use the heat at all, we spend about $25 on hot water, so our March cost for heat was probably about $90. We had the thermostat set to 64 (58 at night and during the day when no one was home) for an average of about 60. Very roughly, then, it cost us $10/degree per month.

To get more accurate than that, we should take into account that each additional degree is more expensive than the last, because the rate of heat loss is proportional to how much warmer than the surroundings you are. There's also the heat that the four adults, one baby, and two cats produce, but that's probably pretty small. Heat from cooking might be significant, but mostly that makes the kitchen warm and doesn't affect the room with the thermostat.

Update 2011-11-21: "the rate of heat loss is proportional to how much warmer than the surroundings you are" does not give "each additional degree is more expensive than the last". Instead it gives "each additional degree is just as expensive than the last".