All the time the heater is burning properly, not situated in a draught, the wick is trimmed so the flame is even and not smoking that's fine, quite safe. Problems can begin when for some reason the heater does start to 'smoke' or give off fumes and that can be caused because there is no ventilation, I'm sure you know that no flame will burn properly without adequate air supply, and if it isn't burning properly it will smoke. If you are asleep for any length of time under those conditions you will be ill or dead. You must have read of people on holiday dying in foreign hotels because the heating was faulty? They didn't die by burning, they suffocated because the heater burned inefficiently,a blocked flue and a tiny pilot light was enough to be fatal.
I'm wary of this because I helped a lady clean the cabin of her boat after she had gone ashore and left a perfectly good paraffin heater burning on board. It took most of the day and countless buckets of hot water and cleaner to remove the smoke damage, like an oily black film, from the inside of her boat because she had closed the cabin down with no ventilation at all. Eventually of course, because of the lack of sufficient air supply the heater went out anyway, but if she had been asleep on board it would have been a sad ending. Well looked after, properly ventilated..no problem at all. Just don't leave them unattended in a tightly closed up space.
