From cityofboston.gov:

The Low Income Home Energy Assistance Program (LIHEAP) provides eligible households with help in paying winter heating bills. The program pays benefits of fixed amounts based on household income and size. LIHEAP operates between November 1st and April 30th, offering financial assistance to residents who are at or below 200% of the federal poverty guidelines.

Local non-profit agencies determine household eligibility based on income and the number of members in the household. The agency then will make payments on your behalf to the primary heat source vendor (oil, propane, wood or coal dealer or gas or electric utility). Special provisions are made for those households whose heat is included in their rent and those living in subsidized housing. Homeowners and renters are both eligible.

Visit the City of Boston's website for more information.