MODERN heating systems are quite dependable, with very little attention needed from the homeowner. When a breakdown occurs, a professional can usually solve the problem quickly.

However, the malfunction known as a puffback is not so easily dealt with. A puffback is an explosion inside the burner chamber of the furnace or boiler (hot-air systems use furnaces, and steam or hot-water systems use boilers).

Although such explosions are usually small and confined to the burner chamber, they can do considerable harm to the heating system. Sometimes the burner will start easily and need only minor repairs and adjustments. But puffbacks usually do more damage, sending soot and smoke throughout the house.

Most puffbacks occur in oil-fired heating systems. In a furnace or boiler fueled with gas, the explosion is usually bigger and more damaging.

A puffback can have many causes but can almost always be traced to a lack of maintenance or a failure to make needed repairs. All heating systems, especially the oil-fired, should be inspected, cleaned and adjusted at least once a year by a qualified professional.

One point of inspection in an oil burner, for example, are the two electrodes that create a spark when the burner starts. This ignites oil sprayed into the chamber through a nozzle.

If these electrodes become coated with carbon or soot or are not adjusted properly, the oil may fail to ignite. In such cases, a control is supposed to shut off the oil in about 30 seconds, but if the control malfunctions the oil will form a small puddle on the bottom of the burner chamber.

The next time the burner tries to start, the excess fuel in the chamber will cause a small uncontrolled explosion - a puffback - and a sudden dis-persion of black smoke and soot throughout the house.

Puffback can also be caused by a partly clogged or cracked nozzle, improper nozzle angle, cracked electrodes, poor adjustment of the air-fuel mixture, a defective spark transformer, shorted ignition cables or dirty or low-grade fuel.

The aftermath is usually the main problem. Walls, ceilings, carpets, furniture and curtains are coated with a fine film of soot and smoky streaks. As a rule, the damage is worse with a forced-air heating system or central air-conditioning, because the duct work provides a path through the house, even into closets.

Cleaning up the mess is not a job for the amateur, but rather a professional cleaning company (many are listed in the Yellow Pages under ''house cleaning''). These concerns use special techniques and materials. For example, attempts to wash soot off a flat-painted wall or ceiling usually leave greasy smears. Professional cleaners use waterless rubber sponges that work like an eraser and absorb the soot without spreading it.

Cleaning carpets, upholstery or draperies can be trickier. They must be washed or chemically cleaned, depending on the material and how dense the absorbed soot is. In extreme cases it may be impossible to remove stains or odors completely.

''White carpeting that gets badly smoke-stained may never get fully restored to its original whiteness,'' said Ron Marchand, head of the Interstate Fire Restoration Corporation in Bayside, Queens. ''But in most cases we can get everything looking like new again - but not if someone has made amateurish attempts at trying to do the job themselves first.''

Costs for cleanup vary greatly. ''The least a small home can get by with is about $800 to $1,000 on the average,'' Mr. Marchand said. ''But where there is clothing, carpeting and upholstery involved, the cleanup cost can run up as high as $5,000 or even $10,000 after a serious puffback.''

For those with adequate homeowners' insurance, the bulk of the cost is usually covered. Most insurance companies are reluctant to pay for jobs by the homeowner; they usually cover labor costs by a professional.

As with most insurance claims, an adjuster must first examine the damage and establish a fair price for the job. To keep a lid on the total cost, most insurance companies have certain maximums for each part of the job. These may be based on such things as the square footage of walls or carpeting, or may be specific amounts allowed for each upholstered piece.