As the summer wears on there many be only one place in Northern Virginia without a case of heat-induced doldrums -- the Fairfax County School System. Between school board resignations and appointments of a major reorganization of the staff, the system is in the midst of a turbulent summer.

The latest changes were three new appointments during the past two weeks.

Most recently, County Supervisor Sandra L. Duckworth (D-Mount Vernon) filled a vacant school board seat with Gerald A. Fill, a senior analyst in White House office on Management and the Budget.

Fill will take office at tonight's board meeting, replacing Ruth D. Dell, who resigned last month.

The newest board member says he brings to the board an expertise in intergovernmental relations -- a talent which may prove valuable during the haggles over state and federal funding for public schools.

Duckworth's appointment of Fill reflected here close ties to the Carter Administration. The Democratic national committeewoman from Virginia, Duckworth is views as one of the state's most powerful Democrats and has been an outspoken supporter of President Carter.

Other changes in the school system were made in the top levels of administration by Superintendent L. Linton Deck who filled both vacancies with personnel from outside the system.

Arthur W. Gosling, an assistant superintendent with the South Orange-Maplewood School system in New Jersey, was appointed to fill the area superintendent's slot in Area IV -- the northern most part of the county.

Gosling replaces Donal Lacey, who moved to the Area II position earlier this month. Gosling will begin his duties Sept. 1.

Deck also announced the formation of a staff-exchange program with George Mason University which will begin in September. In exchange for part-time teaching assistance from Fairfax County's Assistant Superintendent John Schreck and Area I Superintendent Herman Howard, George Mason will loan Albert W. Edgemon to the county for one year.

Edgemon, a education professor at GMU, will design a staff development program, which is expected to be part of Deck's overall plans for streamlining the school administration.