I can't tell if it's fake or not. Some comments said it's totally in line with the laws of physics. But maybe not. 4 rising heat currents must be resulting in SOME turbulence.
In principle, it should work, I think. A glider can stay aloft almost indefinitely but it requires a pretty good pilot. It's hard to accept that a paper airplane could do it with no adjustment in the controls. And the video looks a bit too much like a loop to suit me.
It only flew about one minute or so, that wasn't much and I'd agree it does look like a loop that was edited. Another thing since the stove was turned off the heat wouldn't affect the lift of the plane for much time either.