It depends on the hamster re a blanket over the cage
It's usually ok but some will try and chew the blanket through the cage. I use a big piece of hemp mat on top of ours now. I also put hemp mat on top of the house roof to insulate it a bit. Not sure if it makes much difference or not but in my mind it seems it might!
I have a room thermometer - but usually just gauge the temperature. The heater we have has a built in thermostat so only comes on when the temperature gets below say 14 degrees.
If you have normal central heating on at night and in the morning anyway, it's usually ok overnight unless it's freezing weather. Which it can be in the height of a Uk winter!
These are the snugglesafe's
Amazon.co.uk
This is the towel rail thing I have - just hooked onto the cage bars and the snugglesafe rested in it.
Amazon.co.uk
It's tricky thinking about leaving an electric heater on at night, on a thermostat as there's safety to think about as well - the oil filled ones tend to be safer as they're just like a radiator, and some have an emergency cut out.