Check that the plate which seals off the chimney and the flue system from the room is still making a good seal and that there isn't any condensate staining around the flue pipe which would indicate a problem. This could be cased by either an uninsulated flue liner (or no liner at all), a damp chimney (leaking due to failed mortar joints or a poorly fitting cowl) or poor operation of the stove (too much slumber burning so that the flue gases don't get hot enough to warm the flue, thus creating creosote and / or other condensates).
If your register plate is made of fire board then this should be upgraded to an appropriate metal plate to make it much safer and resilient to any potential chimney fire. Hetas now recommend the use of two plates – one in metal, to help retain any vermiculite filling and resist potential heavy mortar or brick debris falls inside the chimney, with the second, lower one, being decorative but also having the appropriate fire resistance.
Ensure that the register plate still makes a good seal around the chimney aperture and flue pipe so that your newly created hot air produced by the stove doesn't escape to the outside through the chimney.
