As Soviet builders struggle to create a sophisticated industrial society of factories and modern cities across the face of the vast frozen region of northern Siberia, they find that their most troublesome problem is the disastrous effect of the combination of heat and ice.

When the ice within permafrost, the permanently frozen soil of the Arctic regions, is touched by heat and slowly thaws, the still-frozen ground around it cannot absorb the water and the heated earth becomes a mushy quagmire. The source of the heat-be it house, road, railway track or airfield-sinks inexorably into the ooze.

All these objects, at one time or another, have done just that in Yakutia. All it takes is to raise the temperature of the ground above freezing for too long a time, and, like the negligent ice fisherman's warming fire, the object eventually will carve its own path to doom.

The Soviets are learning, at enormous expense and by painful trial and error, the complex variables of avioding what the scientists at the Permafrost Institute here call "creating an active zone" in the frozen turf, so that what they put up will remain standing-perhaps for hundreds of years.

This capital city of 190,000 on the banks of the north -flowing Lena River, 3,700 air miles east of Moscow, stands as a living memorial to the progress. Older log houses and office buildings stand with swayed backs and tumbling corners, and some have sunk to their windowsills over the years. Meanwhile, concrete apartment blocks, standing well above the ground on stilts sunk deep into the frozen earth and insulated from the permafrost, show the lessons learned in building here.

Costly mistakes continue to occur, however. One example is the airstrip in southern Yakutia near Tynda, which was built one recent summer to help serve the new Baikal-Amur Mainline railroad that is being pushed through the taiga forests from central Siberia to the Pacific Coast.

Because the builders had not adequately drained the site or insulated the ground beneath the new runway from the higher heat of its cleared surface, and had not carefully measured the amount or location of ice within the soil, the airstrip transmitted excessive heat into the permafrost, creating an "active zone."

Pockets of ice below melted and by the end of the summer, the airfield had been transformed in places into a boggy marsh, according to Igor Nekrasov, an institute specialist. The site had to be abandoned as another permafrost failure, and a new airstrip was built. The cost of the mistake was added to the already skyrocketing expenditures for the railroad.

With the exception of a few isolated pockets of ground and the beds beneath free-flowing rivers, streams and deep lakes, permafrost is everywhere in Yakutia,. In fact, it covers 43 percent of the U.S.S.R. The permafrost zone envelopes the entire country above the Arctic Circle, and extends southward taking in virtually all of central and eastern Siberia east of the Yenisei River and along practically the entire length of the Soveit-Chinese border.

It ranges in depth from more than 75 feet to more than 1,500 feet, and permafrost scientists think there may be spots where it extends more than a mile into the earth.

Since much of Siberia is plateau and plain, when the summer sun warms the frozen soil it creates seasonal "active zones" where water lies atop the still-frozen subsoil, this turns vast areas of Siberia into mosquito-infested marsh and swamp, although annual rainfall usually is light.

An active zone can vary widely from area to area, or even from one place to another as close as a few one plcae to another as close as a few hundred feet, depending on factors such as the amount of rock in the soil, exposure to the sun, drainage and, perhaps most important, ice content.

Changes in any of these factors-rockslides, drainage, steady accumulation of ice in the layers of earth below-can change the active zone, bring on massive melting and subsidences, which the permafrost experts call "sinks." From the air, the forests appear scarred by this process, with distinct crater-like formations clearly visible throught the snow.

The problems this instability poses for builders sometimes seem insurmountable. Yet the Soviets, despite their inadvertent occasional calamities, have learned to cope. Careful scientific investigation frequently finds that local instabilities rule out the most convenient location for a building, however.

One example is the massive new coal-fired heat and power plant being built at Chulman to serve the Neryungri coal fields in south Yakutia, several hundred miles south of Yakutsk.

The new plant, planned eventually to provide 1.4 megawatts, had to be built 13 miles from the coal pits because permafrost conditions barred a closer site. As a result, the Soviets must build extra railroad tracks to haul coal to and from the plant, and the station itself will be built on massive concrete piles sunk through steam-warmed layers of earth deep into rock or permafrost below the active zone. The plant's floors will be insulated to prevent heat from passing deeper than the present active zone.

The cost of the first stage, to produce 630,000 kilowatts of electricity and 770,000 kilocalories of heat: almost $1 billion, or twice the cost of building a similar plant in European Russia, according to Alexander Andreev, the chief construction engineer. A good part of this extra cost is due to the price of moving materials into the remote area from production centers thousands of miles away, but permafrost adds to the cost as well.

The institute is surveying permafrost conditions along three main routes being considered for a proposed natural gas pipeline that would link the Pacific Coast with the vast new Vilyui gas fields being explored some 1,200 miles to the west. The gas project, which envisions a fleet of liquefied natural gas tankers to carry gas to Japan and the United States, has been talked about for years by the Soviets, and there are letters of understanding on the project among Moscow, Occidental Petroleum Co. and the Tokyo Gas Co.

Nekrasov said the survey teams, numbering just 20 each, would not begin their work until June and the process could take years to complete in the rough forested mountains to the east.

"We will determine the deadline later for finishing the surveys," Nekrasov said.

Though Nekrasov thinks increased development of eastern Siberia ultimately may do some kind of harm to the permafrost, he says the likelihood seems remote for the next 200 to 300 years.

Perhaps reflecting this, the 19-year-old institute, which the Soviets like to say is the only one of its kind in the world and which some Western specialists have said is focused too narrowly on construction problems, has only 10 of its 500 scientists and technicians assigned to ecology work.

In any case, permafrost has been around for at least 2 million years, Nekrasov observed, and seems likely to remain a good while longer. CAPTION: Picture, Soviet youngster stands before apartment houses in frozen Siberia. By Kevin Klose-The Washington Post; Map, no caption, By Richard Furno-The Washington Post