It’s not a given that you will save energy. There’s so many variables to take into account, like how the building is or isn’t insulated, the amount of water in the piping and the size of the piping (thus how much it retains or loses heat and has to be heated up again), other internal heat sources like lights, computers, appliances, water heaters, solar and wind exposure, plus how the boiler functions, like whether it maintains a certain system water temperature based on the outside temperature and then distributes that water to the house via thermostatic valves or if it just runs like a furnace with a simple on/off control. These all have an impact on energy savings as they relate to temperature setback, the question is just what that impact is, which I can’t really answer since they all play on each other.
Here’s a couple anecdotes however. I grew up in a 1920s house with hot water heat (a mix of radiators and some heavy baseboards). Dad generally left the thermostat alone at about 70º except maybe dialing it down 2º or so at night more for comfort than anything. That boiler worked just like a furnace. When the thermostat called for heat, it switched on the burner and pump, and when it was satisfied, it turned them both off. Those round Honeywell thermostats had adjustments for the anticipator that would kick on or off sooner than a furnace or air conditioner to allow time for the water to heat and also to prevent overshooting the set point. As a set it and forget it system, it worked just fine. However, if we’d been away on vacation for a week, when Dad would set the thermostat down to like 57º or something, he’d only turn it up to maybe 65º when coming back because the boiler would just fire constantly until it hit its high temperature cutoff (about 180º I think) while keeping the pump going. If he set the thermostat to 70º when coming home, the system would be so hot after it finally hit that set point that all the residual heat would push the house to 75º or over, so starting lower and keeping an eye on it would prevent that. Programmable thermostats nowadays are smart enough to handle this sort of situation. They ramp up the temperature slowly over two or three hours. It’s the same with heat pumps, so they don’t go into high-power mode if they have multi-stage compressors, and so they don’t engage the very expensive to run auxiliary heating coils.
Other systems work differently though. In my church when I was a kid the boiler would always maintain itself at its high-temperature cutoff point around 200º. This was true no matter the outside temperature, and in fact the boiler didn’t even have any outdoor temperature controls so it could sit there burning up all summer if it wasn’t shut off manually. The boiler itself was insulated and had a damper in the flue so the heat wouldn’t just waft up the chimney. It basically acted as a hot water storage tank. The system was from the mid 1960s, and it used pneumatic Johnson Controls thermostats. Part of that system was a mixing valve that would send water through the boiler as necessary to maintain a system water supply temperature based on the outside temperature. Individual thermostats in each room controlled the radiator valves, and it could even do night setbacks by changing the air pressure of the system from 15PSI to 20PSI, which the thermostats could detect and switch to a separate bimetallic strip (innovative, but not too reliable in the long term). Anyway, being a newer system with thinner pipes and copper fin-tube convectors, the system wouldn’t retain heat like an older one with heavy cast iron radiators and thicker pipes, so there were less warmup and cool down issues. With the boiler always ready to go, and with the water circulating the building at the proper temperature, it made setting back the temperature much more effective in saving on gas.
Currently i’m working on a commercial remodeling project that uses very sophisticated variable refrigerant flow heat pumps with inverter compressors. The client was concerned about setback policies for unused spaces and recovery time. This is in southern Ohio so it does go below zero sometimes, and it’s a 100 year old building with little to no insulation. The mechanical engineer however said that these units can recover from 60º to 70º in 1-2 hours even at 0º outdoor temperature, and this is with no auxiliary heating coils. Bog standard residential heat pumps don’t stand a chance in conditions like that. However, what the engineer did say is that setting back more than 10º on a day/night cycle would use more electricity to recover than simply maintaining an even setting. If a room isn’t being used for many days or even weeks at a time, then yes it makes sense to set back more. Even so, throwing in things like demand metering (where you’re charged extra based on your maximum power draw in kilowatts) can also factor into the equation in unexpected ways.