The State Department will send its own emissary to the conservative Heritage Foundation as part of an unusual effort to improve relations with one of the department's most persistent critics, according to officials of the two organizations.

This peacemaking effort on the home front began with a lengthy visit to Foggy Bottom this month by 11 Heritage Foundation trustees and top executives at the invitation of Deputy Secretary of State John C. Whitehead, who said he has been and continues to be a financial contributor to the conservative think tank.

The decision to assign a career Foreign Service officer as a "diplomat in residence" at Heritage beginning next September is considered a symbol of the State Department's willingness to take the conservative foundation seriously.

"Diplomats in residence" are currently assigned to the American Enterprise Institute, the Council on Foreign Relations, Georgetown University's Center for Strategic and International Studies and the Institute for the Study of Diplomacy. In the past, they have been assigned to the Carnegie Endowment for International Peace and the Rand Corp., according to a State Department spokesman.

The Dec. 6 luncheon and discussions for seven Heritage trustees and four senior staff officials were hosted by Whitehead, with a high-level supporting cast: Under Secretary of State for Management Ronald I. Spiers, assistant secretaries Rozanne L. Ridgway (European and Canadian affairs), Chester A. Crocker (African affairs), Paul D. Wolfowitz (East Asian and Pacific affairs), and other officials.

"When I came to office and I saw that the department was occasionally being attacked by conservative Republicans, I thought that was a shame because I consider myself to be a conservative Republican," Whitehead said in an interview. He joined the department in July after 38 years with a New York investment banking firm, Goldman, Sachs & Co., including nine years as its co-chairman.

Another State Department official said Whitehead undertook his dialogue with Heritage at the suggestion of Secretary of State George P. Shultz, who was concerned about the continued attacks from conservative critics.

"There is no question that differences remain, and I don't gloss over that," Whitehead said. But he added that, over cocktails at the end of the day, there seemed to be common agreement that "the differences were not quite as sharp and certainly not as personalized" as they had been.

Heritage Foundation President Edwin J. Feulner Jr., in a separate interview, called the State Department meetings "useful," but added, "I don't think there was any narrowing of differences."

Feulner called the session with Ridgway "very topical information-gathering on our side" following the late-November summit meeting of President Reagan and Soviet leader Mikhail Gorbachev. Crocker's discussion of African policy provoked "a fairly heated discussion and final agreement to disagree," Feulner said. "We're fairly close on Asia policy" as explained by Wolfowitz, according to Feulner, but he said "we have a fundamentally different perspective" from that of Spiers on personnel and appointment policies.

While saying that the meeting certainly was unusual, one of the department participants said, "it had no impact on State Department policy." He added, "It may be that we didn't dent them, but they certainly didn't dent the State Department."

Whitehead said the meeting provided "not pressure but understanding" to the officialdom at Foggy Bottom. "It's good for people to have their views challenged," he said, and expressed a willingness to have similar meetings with other conservative groups.

As for liberal groups, such as Americans for Democratic Action, Whitehead said, "If they would like to, we'd be glad to do that."