Thousands of poor families in Virginia, Maryland and the Distant of Columbia will share about $65.1 million this winter to help pay soaring fuel bills under a national energy crisis assistance bill signed yesterday by President Carter.

Payments will probably average more than $200 for each qualified family here, and could start arriving in the next few weeks.

The $1.35 billion legislation, combined with $250 million already in the pipeline, making for a total of $1.6 billion, will help some 7 million poor people nationwide.

The complex program will be administered by the Department of Health, Education and Welfare and the federal Community Services Administration through grants to state-level poverty agencies and direct payments to some welfare recipients.

At bill-signing ceremonies at the White House yesterday, Carter said the government will "expedite the distibution of these funds."

Some $400 million of the $1.6 billion total with be distributed Jan. 7 in a one-time check payment to the 3.9 million aged, blind and disabled people who are Supplemental Security Income recipients.

In April, 15,004 District residents, 80,503 Virginia residents and 48,664 Maryland residents received payments under the Supplemental Security Income program.

Another $800 million will be disbursed by the 50 states and the District of Columbia in the line with state plans for residents whose income is no more than 25 percent above the poverty level. This means an urban family of four with an annual income of up to $8,375 can qualify.

While there are no current figures available on the number that might qualify under this program, food stamp distribution figures give an indication of the numbers of families that might: about 40,000 in the District, 4,400 in Montgomery County, 10,000 in Prince George's County, 3,600 in Fairfax County, 2,400 in Alexandria, and 1,500 in Arlington, according to June figures.

State plans, including designation of poverty or community agencies for distributing the heating allowance money, must be submitted to Hew and approved in the next few weeks.

The final $400 million, to be administered separately by the Community Services Administration through local agencies, will cover short-term emergencies such as direct payments for fuel deliveries, clothing, blankets, temporary shelter, food and medicines for persons in extreme situations.

While the $1.6 billion package provides eight times the amount available last winter. HEW officials acknowledge it will not cover all the fuel cost increases anticipated this winter for low-income families.

"All Americans are feeling the effects of decontrol (of the oil industry) and the OPEC (Organization of Petroleum Exporting Countries) price hike," an HEW statement said. "They are paying more for fuel . . . The poor are particularly hard hit. Although their energy consumption is lower than average their expenditures for fuel and utilities represent a considerably larger-than-average share of their income."

Statistics issued by the government yesterday did not show what the emergency heating allowances would be for the Maryland and Virginia suburbs. On a statewide basis, however, the figures showed that Maryland will receive $27.1 million. Virginia $32.1 million, and the District of Columbia $5.9 million.

Supplemental Security Income recipients will be sent one-time heating allowance checks Jan. 7, ranging from $102 each in the District of Columbia and $106 in Virginia to $140 in Maryland. The amounts vary somewhat because the formula for determining payments is based on a complex computation of the poverty-level population and "heating degree days" in each state. Heating degree days refers to the amount the daily mean temperature in a given location falls below 65 degrees -- each degree below 65 is equal to a heating degree day.

The formula is based on 4,779 heating degree days in Maryland, 4,284 in Virginia and 4,211 in the District.

Supplemental Security Income payments for heating costs will range widely in the United States, from a maximum of $250 in cold winter states like New Hampshire and Minnesota to only $34 in Hawaii.

In familes in which two or more members are Supplemental Security Income recipients, the maximum heating allowance is $250.

State-level plans for administering the heating allowance program have not yet been submitted by Maryland, Virginia or the District of Columbia. CAPTION: Picture, President Carter signing $1.3 billion energy crisis assistance bill. By Frank Johnston -- The Washington Post