needs to be 90-95 in there for the first couple of weeks if i'm not mistaken so turning it off even inside your house would mean a significant drop in temperature that wouldn't be good for the ducklings. I've had many heat lamps in the house before, just always made sure they were plugged in to a surge protector and that there was something under them if the glass decided to bust and cause problems. (watch out though, they tend to get awfully smelly after a while)
Is there anywhere else you could put them? possibly a garage or something with a concrete floor? (avoid carpet fires)
You should be able to switch them to a regulat 60watt light bulb after a couple days. I had my last babies in my bedroom for a while and only used a regular bulb. They did just fine and were always warm enough.
Night is when it is most important. Consider that the temperature is at its lowest at a time when you are asleep and not aware if they are very cold. They will peep almost constantly when cold, but if you have then in a room where you are unable to hear them - or if they are not loud enough to wake you - they could easily chill and die with as little as half an hour in extreme cold.
My daughter raised some chickens recently and knocked the lamp as she was watering them- it fell into the brooder and since then it has made me worry even more about how a fire could start- but if set up correctly there is no more risk than any other light bulb in your house. Making sure the lamp is above head hight so they cant knock it with their heads, Keeping the water as far from the lamp as possible - so that when they drink they dont splash drops on it if shaking their heads, and also the before mentioned having the lamp plugged into a surge protector are some things you can do to lower any risk.
Some people recommend using those ceramic reptile heaters to reduce the risk of fire even though they're a bit more expensive. I've never used them, so I couldn't tell you much about them from personal experience. But, yes, you should have a safe heat source available to them all the time until they are older. Make sure they have a cool spot in the brooder, too, in case they get too warm and have to get away from the heat now and then.