On an oil system, expect the technician to check fuel supply, the filter, the nozzle, the ignition, and the burner's safety controls, and to look at the chimney or vent connection. Gas and propane equipment gets a check of the igniter, flame sensor, pressure switch, and venting. A careful contractor tests for carbon monoxide before leaving.
Some no-heat calls end with a replacement. In Mattapoisett, a new oil burner or tank needs a Fire Department permit, propane work needs an LP gas permit, and natural gas work runs through the Building Department's gas inspector. The Fire Department collects its fees before scheduling an inspection, so a replacement takes more steps than a repair.
If the house is a seasonal place you're driving to from elsewhere, tell the contractor who will meet them, where the key is, and how to reach the basement or crawl space. Mention any water on the floor too, since a long outage in an empty house may have frozen pipes.