I agree that an oil-filled is by far the best and safest way to go. I have one that is about 15 years old and that was submerged for several hours during a flood that still works fine.
A couple of comments on their safe use.
1) Absolutely use a thermostat rated for the max wattage output of the space heater. I can't tell you how many times I've seen thermostats only rated for 300 to 500 watts hooked up to oil-filled space heaters that can crank out 1500 watts.
2) Most oil-filled space heaters will have two switches and a rheostat to control the output. It is best to adjust these BEFORE hooking the unit up to your thermostat. The goal is to find what setting heats the room to your liking. For me I only need to have the 900 watt switch turned on and the rheostat turned to about the mid-point. I then turn the rheostat up 1/4 turn and then hook up my thermostat. This way I know that if my thermostat fails the space heater is not going to continue heating. If my thermostat failed at max setting I could easily kill all my herps.
This process can take a while. I prefer to do it on a weekend when I'm home and can monitor the temps.
3) Pay attention to where the space heater is in relation to your cages and set the thermostat's probe accordingly.
4)) I plug a multi-outlet strip into my thermostat and then plug a fan and/or an incandescent light fixture into the strip. Obviously the space heater also is plugged into the strip.
What this does is turn the fan on ONLY when the heater is running. I like this feature because it saves some energy and lets me know how often the heater is cycling at my preferred temps.
I use the light fixture only when I want to see if the thermostat is cycling without opening the door to my quarantine space. I have the light sitting outside the room and can check and see when the light is on. If it's on all the time or rarely on I know to go in and check the temps.