Kiwi is lucky enough to be in the same room as the wall furnace is, so he never needs additional heat around his cage. We, however, do at night since we close off the rest of the house to save money (gas is so expensive, I hate having a gas furnace!). We just use one of those oil filled portable radiators in our room at night and a little space heater in the bathroom when we shower. Neither seem to bother Kiwi, as he spends a lot of time in our bedroom, and my hubby takes him in the shower almost every day. I would personally trust the portable radiator to the space heater any day if I did have to leave one unattended on near Kiwi. The radiator doesn't get red hot, and it's made of metal, so I have more faith in it not catching fire than the space heater (which you can see red coils in while it's running and will burn you if you touch it while it's hot).
If your just trying to save on winter heating bills, you can do what we do. Close off the house/vents everywhere except the birds room. You can use portable heaters in your bedroom/bathroom as needed and just leave rarely used rooms cold. We've found just using the portable heaters as needed, rather than relying on the gas furnace to heat the whole house has cut our gas bill over half, and raised the electricity bill minimally. Plus, Kiwi gets to be in a 70 degree, toasty room all winter long.