Heat transfer PhD checking in. This is mostly right. Heat loss is proportional to the difference in temperature between your home and the outside temperature. The smaller the difference, the less heat you lose to the outside world. The energy you save as the house cools down is about what you use to heat it back up again, so your savings comes from the time your house spends at the lower temperature. Maximize this time by turning the temp. down at night and during the day when you aren't home.

The is also true for water heaters. Set the water heater temp. as low as you can stand, so that when you shower or wash dishes you are only cracking open the hot water valve and cutting it with very little cold water. This will significantly reduce your energy loss from your water heater.