I couldn't recommend any unvented space heater that burns a fuel to produce heat. That fuel, when burned, turns into carbon dioxide and water. They are supposed to have safety features that kill the fuel when oxygen level dips too low. Burning any hydrocarbon fuel (NG, LPG, oil, coal) with insufficient oxygen will produce carbon monoxide.
Besides the possibility of CO (do maintain the CO detector in shape), the fuel combustion produces a pile of water vapor that has to go somewhere. It's first effect is to increase humidity inside the room. If the house air is dry, that may feel good, but the house being dry also means a lot of air leakage through the house. That moisture is going into the wall cavities and attic, where it can condense against the first cold surface. The resulting wetness can result in rot and mold. Moisture isn't an issue in a house designed and built to keep it from being a problem, but such a house doesn't need the space heater anyway.
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