Answer
No, the argument doesn’t make sense. More energy is consumed if the house is kept at constant temperature.
Work Step by Step
In winter, a warm house loses heat at a higher rate than a cooler house. In a 24-hour period, a house at constant temperature loses more heat to the cold outdoors than a house whose thermostat is turned down at night. The furnace must replace all of this heat.
Summary: in following the magazine’s advice, the energy usage in the morning decreases, but the usage at night increases greatly, and overall, more energy is used. Note: this advice might make sense economically if the night utility rates are lower.
