The Fairfax County School Board predicted a $3.5 million budget deficit yesterday, most of it attributable to higher energy costs.

The County Board of Supervisors, which met with the school board yesterday, allocated $451,000 from a reserve fund to make up part of the shortfall. Then, after school board members said they were still alarmed, the supervisors voted to have the county executive explore ways of making up a large deficit.

The effect of such a deficit "could be a real shocker," declared school board member Nancy Falck of the Dranesville District. "It might entail the problem of paying teachers' salaries. It may involve charging a fee for textbooks . . . we really have no idea of the extent of the problems."

The supervisors indicated that the schools will in any case have access to an additional $1.8 million county budget surplus if it is needed. But Board Chairman John F. Herrity said the prediction of a deficit is premature.

"Education is one of the primary concerns of this county." Herrity said, "but we have to deal with hard facts and hard projections, and we won't have that until the mid-year school budget review in January."

A $2.57 million increase in energy costs was estimated by Myron E. Cale of the school board's financial services department. He said the board expects to have spend $1.7 million more for fuel oil in the coming school year, $366,200 more for electricity and $381,000 more for equipment maintenance and transportation.

Falck and school board member Ann Kahn of Providence District said there are few financiaal alternatives available to their board if the deficit materializes.

"Eighty-six percent of the school budget is contracted for teachers' salaries and it would be illegal to fire them or lay tham off half way through the school year," Falck said. "There is simply very little we could do."

Almost $1 million of the projected $3.1 million deficit would be the result of a cutback by Congress of U. S. aid to school systems that teach large numbers of children of federal workers.

Neither the House of Representatives nor the Senate have voted on the so-called impact aid cutback proposal, which is made every year. The supervisors are already committed to make up any cut in this aid.

As they had pledged to do, the supervisors restored a $400,000 budget cut yesterday to prevent a cut in shool busing service that angered many parents.

Supervisors Warren I. Cikens (D-Mount Vernon), who is not seeking reelection this fall, noted that the current board is assuring the schools that money will be available to make up a deficit, "but this board is not the board that will have to find the money." Every seat on the board of supervisors will be up for election in November. "We're making assurances but we don't exactly know where the money will come from." Cikens said.

The motion to have the county executive explore ways of dealing with a large school deficit was made by Supervisor Audrey Moore (D-Annandale). It passed on an 8-to-1 vote, with John P. Shacochis (R-Dranesville) voting no.