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Blown insulation above the soffit? You'd need to check the design of the roof and ventilation etc in the ceiling void.
Mind you given the thought that went into designing that room with regards to the ceiling height it's possible that a builder threw the roof together in an afternoon whilst not looking at plans, stood back, looked at his work then said "fuck it that'll do" and went to the pub.
My place has a two story extension on the back with a conventional flat roof. There is clearly no insulation in the roof space because the ceiling is cold to touch and the radiators cannot heat the room adequately. The ceiling is low and the door only just clears it. I was hoping I could line the ceiling with insulation material that can be skimmed with plaster and painted - the tricky thing being that there is only 25mm clearance above the door.
Any recommendations?