Maybe birds. Once a bird starts down a flue it can only get to the bottom, because they can't do a vertical take-off and they can't climb.
If it is a bird, they don't take long to starve to death.
If you do dismantle the heater to let it out, open all the windows and doors first, and draw the curtains/drapes over the unopening ones. -Unless you like the idea of a panic-stricken sooty bird in your lounge.
Chimneys originally built for open fires often have a side-step just above the fireplace. Maybe it is sitting on there.

I think birds fall asleep and topple off the perch. It wouldn't matter up a tree, but chimneys, now.....