I personally don't feel safe sleeping in a canvas or nylon tent with a heater running, unless it is direct vented outside. Even cracking the door a bit to let in fresh air does not abate the potential fire hazard. I know the modern heaters, such as the Little or Big Buddy models have O2 sensors. I trust they work, for the most part.
In the old days our strategy would be to fire up the lantern, bring it in the tent for a few minutes to warm things up, kill it, and set it outside. I've now done the same thing with a Little Buddy, except I didn't put it outside -- only turned it off. That way there is little chance it will cause a spark overnight or deplete all the oxygen any further.
Just my thoughts.