When a fireplace and chimney are designed and built, the designer usually has a particular sized fire and fuel in mind.
If a fire is too small or burns too cold, you may well have a problem.
While the idea of burning wood seems to have caught the Governments imagination, the reality is not always that good.
If your chimney is old, It may not have been parged, or lined to a satisfactory standard, it may be subject to condensation.
If wood is not seasoned and dry, if the chimney is not hot enough this may well lead to deposits of tar.
If coal and wood are burnt at different times, the coal will product sulfuric acid the wood condensation and the two will combine to dissolve the lining of your chimney, with the wood leaving deposits of tar, this can lead to a chimney fire.