I hear you chap, and your probably getting "woman grief over this" but also consider this
People used to survive without central heating at all not so long ago
You may be better getting a small thermostat controlled heater and placing it in the babies/your room (wherever said tot currently is). One of the oil filled rads would be perfect. You dont need it to be hot, just not cold, you may be surprised that it doesnt come on a lot at all as its not really getting cold, just cool.
IIRC overheating was deemed way more dangerous for infants especially very small ones than being slightly cool.
You will use a lot of gas heating the house as you are for that hour at night. It will literally go all out for an hour using quite a bit of fuel, if its not then you didnt really need it on anyway.