It is almost impossible to burn paint with the PC (assuming you are following all precautions), but if you somehow manage to burn it, the only thing you can do is re-paint. Burnt paint is really just no paint left, or one layer gone
When you burn through it is really hard to just use touch up paint on it. Touch up is a really thick paint meant to be touched into cracks. burnt paint is real smooth and flat and generally the size of a penny and larger. An airbrush is the best bet at repairing it. then yes, wetsand and compound to get the paint back to even, but it is really a PITA