Baking cakes and bread in a wood-fired oven can be a bit difficult: things tend to cook too quickly on the outside while remaining undercooked or raw inside.
To get round this, it is a good idea to cover the cake or bread with foil for most of its cooking time. It is best to use a cake tin with high sides so that the cake mixture does not stick on the foil when it rises.
Through a process of trial and error, I have found that if a cake needs to be baked for 40-45 minutes, then what works best is to cover it with foil and bake it for 15 minutes. Have a look and if it seems to be cooking too quickly or too slowly, move it forwards or backwards in the oven. Turn it 180º and cover it again for another 15 minutes before having another look
Turn again through 180º and remove the foil. Let it cook for a further 5 minutes before checking. If it seems to be browning too quickly, replace the foil otherwise leave uncovered for another 5 minutes.
Test the cake and if it is still not done, put back in the oven for another 5 minutes.
A wood-fired oven retains the heat a lot better than a conventional oven so there doesn’t seem to be the same problem of opening the oven door and letting the heat out.