Evidence is mounting that closing the blinds can reduce the rate of heat decline—at least when the wind is mostly still. The figure compares the heat loss rate to the indoor-outdoor contrast. Higher rates are bad.
Closing the blinds keeps reduces the temperature loss rate by about 0.1 degree F/hour. Integrate that loss rate over the course of the night and closing the blinds keeps the house 1 degree F warmer.
To keep the house 1 degree F warmer by turning up the thermostat 1 degree F during the night would increase energy use about 1%. This could save as much as 3% on the heating bill according to many sites who uniformly cite miserably.
My gas bill is about $70/month during the winter, assuming 4 months, I’ll save $8.40 per year by closing the blinds. This should pay for the blinds in only a little over 120 years.
I’ll continue collecting data, and may update this if the results change. Your mileage may vary.