Hirings and promotions in the D.C. Fire Department, virtually frozen since a discrimination claim was lodged by black firefighters, will soon be thawed by the hiring of 88 recruits and the elevation of about 45 department members to higher ranks, Acting Fire Chief Theodore R. Coleman said yesterday.

Coleman, named to his post last week by Mayor Marion Barry after the bizarre disappearance and subsequent retirement of Chief Norman Richardson, made the disclosure in one of a series of interviews with individual reporters. An aide to Coleman said he had been barred by superiors at the District Building from conducting a single news conference for all the media.

While he is a candidate for permanent appointment to the top post, the 55-year-old acting chief said Barry had made no commitment to him. But he said Barry granted approval for hiring of 88 new firefighters, which he plans to do April 12.

In about three weeks, Coleman said, he also will announce about 45 promotions, including those of three assistant chiefs, eight deputy chiefs and numerous captains and lieutenants.

The department's last major round of promotions came in 1980, bringing protests from the black Progressive Firefighters Association that blacks were slighted. In mid-1981, the D.C. Office of Human Rights issued findings that the department was continuing systematic discrimination against blacks in hiring, promotions and assignments. Following protests from white firefighters, hearings on that issue are continuing.

Coleman refused to take any questions about Richardson or the racial discrimination case.

Coleman, a resident of Fort Washington in Prince George's County, has been a member of the department for 29 years. He said that, as a black, he never encountered difficulty in moving up in the ranks. "It was a case of taking exams and working hard," he said.

If named chief--his goal ever since joining the department--he said he would move into D.C.

During yesterday's interview, Coleman received a call from City Administrator Elijah B. Rogers, whom Richardson had accused of meddling in departmental affairs. Coleman picked up the phone and was heard to respond, "Yes, sir . . . yes, sir . . . yes, sir" to what Rogers was saying.

Asked about that, he replied that Rogers "is my boss and that's the way I am going to be, and that's the way my men are going to be."