Unfortunately not. I added some lime scale remover into the head and left it for several hours and when I returned to try turn the thermostat it didn't appear to do anything. It's a little difficult as you can't see anything but I really don't feel like anything is turning in either direction. I'm also a little worried about stripping the thermostat screw.
Not sure what to try next – I'm thinking it's one for a plumber.
Thanks again for all your help.