If you own the place, you could repaint them with heat resistant paint, though you would have to make sure the heater was switched off and ensure that the heater circuit is isolated at the consumer unit and the storage heater cold (If you have any serious concerns about your ability to do this....Don't do it). Before removing the front cover (most tend to be held on with a couple of screws on the bottom of the front panel (DO NOT remove the wall support screws though, unless you want to risk broken bones and / or a broken heater) If you can find a model number, some here will likely know an answer on how to remove the front panel.
scuff the surface down with some high grit sandpaper 180 grit for example, to provide a key, give it a wipe over with a damp cloth to remove the dust, let it dry, then apply the paint in thin coats, especially if using spray paint.
Best to do rubbing down and painting outside if possible, though be aware of wind which will blow the spray away and blow dust onto your paint
My old man did similar a few times when he had storage heaters as the paint on some of the heaters discoloured due to age and repeated heating.