LIHEAP (New Jersey's Low-Income Home Energy Assistance Program)  helps homeowners as well as renters who pay their own heating bills.
Income limits - single person can earn up to $1980/mo; family of four up to $4050/mo.
Benefit is determined by income, household size, fuel type and what part of the state the client lives in.
With gas or electric, payments go directly to the utility company; oil the check is usually made out to the fuel supplier and applicant.

Families must apply for benefits in person through local agency offices and they have to recertify each year.  For a list of Energy Assistance Programs and income levels, go to http://www.state.nj.us/dca/divisions/dhcr/offices/heausfincomefact.html or call 1-800-510-3102.