During a recent murder trial in Fairfax County, some jurors sat bundled in coats, gloves and hats because of the courthouse's malfunctioning heating system. Periodically, the same jurors had to raise their hands to indicate to the judge that they could not hear the testimony in the case. Witnesses in the case waited sometimes in the crowded courthouse hallways until they were called to testify.

It is because of such conditions in the 177-year-old structure that Fairfax County officials have proposed an $18.7 million bond issue to build a new county courthouse. A referendum on the issue is scheduled for Tuesday.

If the bond issue is approved, the new courthouse for the Circuit and General District courts will be built near the intersection of Chain Bridge Road and Jones Street and connected to the new jail now under construction.

The historic old courthouse a block away, once visited by such figures as George Washington and George Mason and which was a Union outpost during the Civil War, would be maintained. It would house the Juvenile and Domestic Relations Court along with some county offices.

Court officials say that if the bond issue is defeated, the county may have to build the new courthouse out of the county's general revenues on a pay as-you-go basis. In 1971 county voters rejected a $12 million bond issue that would have built a new courthouse, among other things.

Under Virginia law, Chief Fairfax Circuit Court Judge Barnard F. Jennings could order the county to build the courthouse if the bond referendum failed."It's a badly needed building," he said.

Financing the courthouse on a pay-as-you-go basis would necessitate raising the county property tax rate, according to county officials.A taxpayer owning a home valued at $62,000 - the median price in the county - would find $125 added to his tax bill, which last year was $1,078.

If the bond sale is approved in the referendum, no property tax increase would be required, county officials say, as long as the county sells no more than $46.6 million worth of bonds annually. Sale of more bonds would require a tax increase to pay increased interest payments to bond purchasers.

The county officials say they don't plan to exceed the $46.6 million figure.

Harley Williams, president of the county Taxpayers Alliance, which is opposed to the courthouse bond issue and has consistently opposed bond is issues in the past, disagrees. He said the county would have to sell more than $46.6 million worth of bonds a year to finance the projects the county wants as part of its capital improvement program.

Judges, lawyers, other court officials and jurors complain about the present courthouse.

They say some of the court rooms are so small that it is impossible for lawyers and their clients to talk privately and for judges to hold bench conferences without being overheard by the jury.

They also complain that no adequate place exists where jurors may wait to be called, where they can be insulated from contact with witnesses, the public, or, in some cases, the accused.

During the recent trial at which James Breeden was convicted of murdering four persons in a Roy Rogers restaurant, the defense attorney asked the judge to order the jurors to wear identification badges so that people in the crowded halls would know who they were and refrain from discussing the case in their presence. The judge denied the request.

Part of the existing courthouse dates back to 1800, and the county has declared the oldest courtroom a historic monument. Nevertheless, the 177-year-old courtroom is used to hear cases, since the number of judges with cases on the daily docket often exceeds the number of courtromms.

Court records are also a problem, according to Circuit Court Clerk Jim Hoofnagle. He said the records have outgrown the capacity of the record and file rooms. Heaps of records, some of them of historic interest, are stored in the attic.

The wills of George and Martha Washington have been kept in the courthouse vault, which is deemed insecure. The Virginia General Assembly last week voted to allow Hoofnagle to transfer the wills to a county museum where they could be kept more safely.

William of Taxpayers Alliance maintains that the problems in the present courthouse could be alleviated by better management. He said the Juvenile Court could be transfered to an empty school building and the traffic cases heard in the General District Court - about 70 per cent of its caseload - could be decentralized.

The Rev. John M. Wells, minister of the Reston Community Church and a lawyer, said he also favors decentralizing the court system. "If minor traffic offenses, the petty misdemeanor cases and the juvenile cases were removed from the present courthouse, the problems of overcrowding, parking and congested hallways would disappear," he said.

Wells, who opposes the bond issue said traffic cases and petty offenses could be handled by the magistrate at police stations. He said juvenile cases could be handled in the county's 22 high schools. "It would necessitate some circuit riding by our judges, by some clerks and by some benefits," he said.

Wayne Lynch, co-chairman of a citizens group working for approval of the bond issue, dismissed decentralization as "just a method of buying time." He said the county would still have to face the same problems in a couple of years.

County officials said they have no reason to believe it would be cheaper to move Juvenile Court than to renovate the old courthouse.

The lightening of the caseloads in Circuit and District Courts would have to depend on action by the Virginia General Assembly, court officials said. The total caseload of those two courts has more than tripled since 1970, they said.

The fairfax County Federation of Citizens Associations and the League of Woman Voters support the bond issue. CAPTION: Picture, Fairfax County courthouse, completed about 1800, will be used for Juvenile and Domestic Relations Court and county officers if new building is approved. By Craig Herndon - The Washington Post; Picture 2, This photograph of Fairfax Courthouse was taken in 1863 while Union troops were using it as a stable. By Craig Herndon - The Washington Post; Picture 3, File cabinets abound in Fairfax court clerk's office. By Craig Herndon - The Washington; Picture 4, Restored interior portion of Fairfax Courthouse, By Craig Herndon - The Washington Post