MALDEN, Mass.—On a muggy, summer weeknight here, workers were preparing for winter: Riding a specially modified truck along tracks that carry subway trains to Boston, they planned to upgrade thin heating elements that melt snow off the third rail.

Such fortifications for the Massachusetts Bay Transportation Authority, known locally as the T, are part of an $83.7 million triage plan launched after record-breaking snowfall triggered major failures on the nation’s fifth-largest transit system early this year. Area residents rely...