The price of residential heating oil, which fell below $1 a gallon last July for the first time in many years, is climbing back fast despite stable world prices for crude.

While fuel prices normally increase in anticipation of cold weather, prices appear to be rising faster this fall than in recent years, according to Department of Energy data.

In both 1983 and 1984, prices of heating oil dropped about 8 percent between January and August, and then rose by less than 2 percent between August and December, according to the Weekly Petroleum Status Report published by the Energy Information Administration.

The average price per gallon nationwide was $1.049 per gallon in January, and fell 7.4 percent to 97.1 cents in August, the latest month for which EIA data is available. (The figures do not include taxes.)

In the spot market, where prices reflect daily trading rather than long-term contracts, heating oil reached its yearly low of $28.55 a barrel in early July. As of mid-November the price per barrel had risen almost 30 percent to $37.06. (A barrel contains 42 gallons.)

A spot check yesterday of a half-dozen fuel oil suppliers in the Washington area showed that one company had raised its prices 7.2 percent since August; another, 3.5 percent since October. The current price quoted ranged between a low of $1.1158 per gallon and a high of $1.219 per gallon, including taxes.

"Our suppliers have called up every day for the past week and a half to boost their prices," said Roscoe Price, manager of Mockabee's in Forestville, Md. "

A key reason for the upward movement in prices is the shrinkage of inventories, both in this country and Western Europe. Oil companies have lowered production and imports to try to match a steady decline in the demand for petroleum, due to energy conservation and switching by households and businesses to other fuels.

EIA estimates that the total supply of distillate fuel (heating oil) on hand Nov. 15 was 129.3 million barrels. That compares with an average inventory of between 160 and 180 million barrels usually on hand at this time of year. U.S. imports of crude oil and petroleum products declined more than 10 percent in the year ending October 1985.

Another factor is the increasing vulnerablility of prices to sudden changes in market conditions, because of the increasing volumes of products that are bought on a short-term basis. Industry officials noted that warfare had damaged Persian Gulf oil facilities in September, and that caused nervous traders and purchasers to try to lock in supplies, bidding up short-term prices.

The current upward move in prices appears to be a paradox, an industry official said, because Saudia Arabia has boosted its production by more than 1 million barrels a day, to increase its income. That additional production is just now reaching U.S. ports, however, industry officials noted.

In the meantime, the trend in heating oil prices is upward. Mockabee's, which had boosted its price to $1.20 this summer, bucked the trend a few weeks ago by lowering it to $1.158. "Nobody's buying that much oil with this [warm] weather," Price noted. But he predicted that once the winter sets in, "We'll be back up there with everybody else's [prices]."

An employe of A-Fuel Oil Co. in Northeast Washington said the company was trying to hold the line, but that its wholesaler was raising prices twice a week. "It's been going up rapidly. Last year the price didn't change that fast," he added. After a price increase at midnight Wednesday, A-Fuel now charges $1.179 per gallon.

Mary Welter, of Thomas W. Perry Inc., serving Montgomery County, said prices have climbed from $1.10 last August to $1.18 today. Bill Knop, a dispatcher with Robert Shreve Co. in Arlington, quoted the company's Oct. 9 price at $1.156; yesterday it stood at $1.196.

The consensus in the industry is that oil prices will fall again, as soon as the heating season ends next spring and demand declines. If this proves to be a mild winter, prices could turn downward as early as January, officials said.