Energy Secretary James R. Schlesinger has sent a draft presidential energy address to the White House that calls for "mandatory" conservation measures including a ban on Sunday gasoline sales, lower thermostat settings, and a wide range of longer-term energy initiatives, according to administration sources.

The speech, described by one energy official as "a very rough, and very early, draft," is now at the center of a mounting Cabinet-level debate over how President Carter should deal with the Iranian oil shutdown.

Over the last week, Schlesinger has warned that the Iranian oil shutdown, now reducing the nation's energy supply by about 3 percent, is "prospectively more serious" than the 1973 Arab oil embargo. Department of Energy officials, meanwhile, have urged a major presidential energy address calling for symbolic, yet mandatory, conservation measures to make up for lost Iranian oil, and a new and more vigorous emphasis on the administration's long-term energy programs.

Treasury Secretary W. Michael Blumenthal, meanwhile, has been pressing Carter "to take a low-key approach" and not call for mandatory conservation measures, because of the effect such a speech might have in driving down the value of the dollar in world money markets.

The State Department has also opposed a presidential speech on the Iranian oil situation, for fear that it would have an unsettling effect on leaders in the other industrial nations who are nervously watching tight oil markets and rising prices resulting from the Iranian upheaval.

Energy Department officials are chafing at official announcements yesterday by Abu Dhabi and Qatar, two increased their prices 7 percent above official cartel price. DOE and State Department officials over the last weeks have been saying that they expected some of the cartel members to take advantage of the tight oil market and raise prices to increase oil revenues. In some cases, Abu Dhabi and Qatar will be charging $1.20 more per barrel than the official price of $13.34.

Gasoline and heating oil prices could go up a penny or more a gallon if other OPEC members follow suit. DOE has said that gasoline prices will go up 9 to 12 cents a gallon by the end of 1980.

As for the proposed energy speech, however, White House officials say that the president is not expected to decide whether to give a full-blown energy speech based on the Iranian oil shortfall "for a couple of weeks." "The president is not personally involved at this point," said one official.

Some weeks ago, White House officials say, domestic adviser Stuart E. Eizenstat proposed that Carter's forth- coming Georgia Tech speech, scheduled for Feb. 20, be devoted to energy. Since then, however, Carter and his advisers have decided to devote that address to the strategic arms limitation treaty (SALT).

Schlesinger and other administration officials have been under strong pressure from Congress to take action in response to the Iranian situation, Sen. Henry M. Jackson (D-Wash.) and others in Congress have also called on Carter to make the case for mandatory conservation measures such as Sunday gas station closings and oil allocations in a nationally televised address.

Schlesinger has told Congress that the DOE will send its standby gasoline coupon rationing plan and other mandatory conservation measures to Capitol Hill on Feb. 26. Working estimates of potential oil savings from Sunday gasoline station closings are set at 150,000 to 300,000 barrels per day; restrictions on thermostat settings on air conditioners and heating devices are expected to save from 200,000 to 350,000 barrels a day. DOE officials, however, stress that these estimates are "illustrative" and would ultimately depend on consumer response.

One irony about the debate over whether Carter should again make a major energy address -- his last was the April 20, 1977, speech when he unveiled his "moral equivalent of war" appeal to enact the national energy plan -- is that last December the president's closest political advisers, including Hamilton Jordan, had pressed Carter to back away from the energy issue as the White House geared up for his reelection campaign. Consequently, Carter's State of the Union address contained only 12 words on energy.

The Energy Department also did not fare well during negotiations over its fiscal 1980 budget with the Office of Management and Budget, when it pressed for increased spending for energy research and development. OMB cut the department's initial requests by almost $3 billion, and sharply cut back budget requests for coal research, and other new technologies.