President Carter's long-running federal hiring freeze is showing definite signs of a thaw.

Back in March the president told government departments they could fill only half of their vacancies until further notice. During the first six months of the freeze, the number of full-time federal jobs declined more than 20,000, but in recent months the number of federal workers in some agencies has gone up.

Despite the hiring freeze the legislative branch of government -- Congress, the Library of Congress, Government Printing Office, etc. -- has hired, and fired, as usual. The number of Senate and House employes actually increased whilel most other government units were shrinking. That trend temporarily has been reversed, because so many members of Congress lost reelection bids, throwing thousands of their aides out of work.But hiring is on the rise, again, on Capitol Hill.

Downtown, the Defense Department, the biggest government operation, has increased its hiring. Other departments also are loosening up, although all deny that they are trying to beat this freeze, or stock up in anticipation of a total freeze from President-elect Reagan. But the numbers in some agencies are going up, whatever the reason.

Defense started out the 1980 year with 910,263 full-time, permanent employes. That number dropped about 1,000 the next month, another thousand the next month, then went up another thousand after the Carter freeze. Officials say that is because the president "telegraphed" his intention to freeze and it gave federal agencies time to send out "commitment letters" promising jobs to people. (Word of the coming freeze, for example, was reported here three weeks before it was actually confirmed, announced and imposed.)

Carter said that persons who had received "commitment letters" from agencies could be hired, anyhow. Defense alone had made more than 12,000 such commitments, in anticipation of the freeze.

The Pentagon got in the spirit of the freeze by mid-year, and actual full-time permanent employment dropped nearly 12,000 jobs. It hit a low of 892,221 in August, so low that military commanders in many installations began pulling troops out of combat and support jobs to handle clerical and housekeeping jobs formerly done by civilians. In September the number of Defense civilian jobs went up to 897,922, and the October total will be 900,971 when official figures are released. With a freeze on, the question is how come?

Overhiring is a kind of double-bookkeeping via a crystal ball. What you do is estimate how many vacancies you will have next month -- through death, retirement and resignation -- and then immediately hire people (within the freeze limits) to replace people you anticipate will leave.

In recent weeks other federal agencies have contacted people who applied to them months ago and told them to hurry on down and be sworn in. Some of those persons hired say they were told they were being hired because federal agencies anticipate Reagan will slap an absolute freeze on hiring when he takes office, but Reagan aides say no final decision has been made on what kind of freeze -- if any -- he may impose.