Safety cover for exposed brick exhaust inside a bedroom
For a longer term solution it might be worth considering two investigations.


Look at building out the wall around the exposed brick in the room. This could be built to sit a couple of inches (4 - 5 cm) away from the brick to create a dead air space behind the wall to isolate the room from the temperature variations of the bricks. Such wall structure with its "studs", however that is configured, offers a lot more options for installing safety measures.
Look into see if it would be possible to retrofit the chimney with an inserted double or triple wall stainless steel flue liner. The easiest case is one that would fit within the existing flue of the brick chimney. More invasive rework involves removing the brick chimney down to some level and replacing the stack with the rigid style multi-wall stainless steel stack that is supported with a new wood structure then sheathed appropriately for interior or exterior surfaces.