Spread a drop cloth across the floor.
Wash off the dust, dirt and soot from the walls with warm, soapy water and a sponge. If this does not work, try a soot remover. Wash down the areas with clean water and allow the surfaces to dry.
Line the trim at the top and bottom of the walls with painter's tape.
Open a can of lacquer-based primer with a screwdriver. Mix the primer with a paint stick, then pour the primer into a paint tray. Dip a paintbrush or roller into the primer and paint over the thermal tracking stains. Allow the primer to dry before applying a lacquer-based top coat.