Space heaters are safe if used right. Extension cords are a bad idea unless you use a heavy duty shop cord, but I still would avoid it if possible.
Another area to keep an eye on is the plug-in connection. Spread the prongs on the heater's plug so you get a good, tight, snug connection. You should replace worn out outlets that don't hold the heater's plug firmly in place.
What happens in the connection area between the plug & outlet is that the flow of electricity heats up the connection & the plastic housing of the heater's plug, allowing the prongs to flex and the on/off surges of the electrical flow causes the prongs to flex. This can lead to arching and shorting. This applies to any electrical heater - space heater and/or radiant oil-filled.
They're all safe as long as you follow the above guidelines. At least, that's my humble opinion.
I personally like the way the radiant oil-filled heaters heat up a room better than most fan-forced space heaters. Be sure to get one with a built-in thermostat. Well worth the few extra bucks. By far.
Randy (Art In Scales) has got a somewhat elaborate setup that seems to work really well. Just depends on how far you want to go.
One thing to keep in mind is how heaters lower cage humidity. You might find that you'll need to incorporate a humidifier/vaporizer. If I'm not mistaken, I think Randy does.
Have a good one!
HH
-----
Due to political correctness run amuck,
this ol' hillbilly is now referred to as an:
Appalachian American

www.natures-signature.com