On an oil system, expect the technician to check fuel delivery, the filter and nozzle, the ignition, and the safety controls that caused the lockout, then test combustion before leaving it running. On a gas furnace or boiler, the focus is usually the igniter, flame sensor, pressure switch, and venting.
If the fix means replacing an oil burner or tank, Hanson's Fire Department permit schedule covers that work, and gas piping is inspected by the town's plumbing and gas inspector, who requires a plumber or gas fitter with a Massachusetts license on site. A contractor may restore heat first and handle the permit for the permanent repair afterward; ask how they'll handle it.
Ask the technician to explain what failed and whether the outage, the fuel supply, or age caused it. That explanation tells you whether to plan for a repair, a backup power hookup, or a replacement before next winter.