I’ve recently moved from a country which doesn’t tend to have central heating (except perhaps in the south), so am new to the whole concept.
Can anyone tell me which of these two scenarios is more ‘fuel-efficient’?
Scenario one: The boiler is set to a high temperature, but the radiators are set to low
Scenario two: The boiler is set to a low temperature, but the radiators are set to full
Thanks in advance for any assistance. 
Hm, our boiler is for heat and hot water, so it stays a constant 130 fahr, and the thermostat circulates water in the system according to the air temperature. In central heating, y ou set the temperature for what you need the temp to be. When we are short on heating oil we set it at about 45 so the pipes dont freeze but siince the fire is burning most of the time we are awake, the heater only cycles on between probably midnight and 5 am.
The question is sort of apples and oranges, more realistically is what is the most efficient way to run the central heat, turn it down when we are gone/asleep and raise it to comfy when people are home/awake or leave it at a constant setting …
It’s most efficient to have a small difference in the setback of your thermostats. Heating a large thermal mass like a house takes a lot of energy, so if you are setting the thermostat for 55 at night and 68 during the day, you’re going to burn a lot of fuel.
Are the radiators steam or hot water?
Are you saying it would be more efficient if the nightime temperature were higher?
Hot water.
The simple answer is ‘yes’. The more complicated answer involves the energy star rating of your house and how efficient your boiler/furnace is. In my case, our place was built in the 70s, with very poor air-sealing and using batt insulation on 2x4 studs. Leaks like a sieve. In addition, the front area is vaulted, which means a hot roof. To complete the picture, the boiler is a Pennco (not made anymore), installed when the place was built. So if I set the thermo back too far, the house cools down rapidly because of poor insulating factors, and it’s a real bitch to get it back up to a comfort zone, since the boiler has to overcome the continuing heat loss and heat the thermal mass at the same time.
The norm in the UK is for the radiators to be on full, then use the thermostat and the boiler temperature to make other adjustments. It’s also quite normal to have the heat completely off at night and when nobody’s in the house, and for the boiler to come on about an hour before you get up or get home from work. With gas and oil prices the extortionate prices they are over here, unless you’re loaded, this is quite necessary - our relatively diminutive houses mean that few of us experience the reheating issues mentioned by ChefGuy.
It’s certainly possible to postulate furnace issues that could make this so, but thermodynamically, it isn’t. Heat loss is closely related to temperature difference, and thus the BTUs expended at night to keep the house warmer will be greater than what’s necessary to re-warm the house in the morning.
To put it another way, the air outside your house will be warmer if you keep your house warmer. This is an indication of the loss of energy from your house. Higher loss = lower efficiency.