Turn off the Coleman furnace. Turn off the gas line if it's a gas furnace. Allow the furnace to cool.
Open the burner and firebox service door using a screwdriver.
Vacuum the burners, located below the firebox, and the heat exchangers (a series of tubes located inside the firebox at the top) with the brush attachment. Scrub the heat exchangers with the brush to remove any stuck-on soot or ash. Wet the cloth and wipe between the heat exchanger tubes to remove any built up soot.
Open the blower's service door. Vacuum the blades of the blower's fan to remove any dust. Wipe the blades with a damp cloth. Lubricate the fan's axle with 2 drops of SAE-10 oil.
Close the service doors and turn the furnace's power and gas back on.