From the Rocky Mountains to the Atlantic Ocean, infernal heat and dry weather are seriously threatening the corn and soybean crops that underpin the U.S. farm economy.

The unexpected drought comes on top of the administration's payment-in-kind, or PIK, program, which had already reduced expected production of grain and other major crops. Together they could sharply increase food prices next year on everything from beef and pork to eggs, soft drinks and cooking oil.

Long-range weather forecasts show little relief ahead from the dry heat, and specialists at the U.S. Department of Agriculture see the next two weeks as critical in shaping the 1983 corn and soybean crops.

"It is a discouraging picture," said Lyle Denny, a USDA meteorologist. "The five-, 10- and 30-day forecasts for August all call for less rain and warmer weather than normal."

A former Democratic official of the department added: "If this corn crop goes down the tubes, you'll hear people calling this administration's payment-in-kind program one of the most colossal blunders of all time."

Corn, a key ingredient in meat, poultry and milk production and hundreds of industrial uses, is a common denominator. Under the PIK program, farmers have idled about 30 percent of their corn acreage, with the crop expected to be about 6 billion bushels, compared with last year's 8.4 billion.

The PIK program, giving farmers surplus grain in return for not planting, has already pushed corn prices upward--one of its intended aims. But weather jitters have hit markets in recent days and fueled the price spiral, leading some analysts to predict rapid rises in meat, poultry and other basic food prices.

Rep. Cooper Evans (R-Iowa) predicted last week that the USDA, given the tightened situation, will abandon plans for a PIK program for corn in 1984. "By fall, the government's corn bins will be empty, market prices will be up and our farmers will be gearing for full production in 1984," he said.

Meanwhile, the weather situation is this bad:

* Although the first official USDA 1983 corn harvest projection won't be out until Thursday, specialists there expect losses to be heavy because of drought in the key midwestern Corn Belt states. Some private analysts predict the national crop will fall 1 billion bushels short of expectations.

* Experts at Iowa State University call the situation in their state worse than 1980, with forecasters predicting the state's corn yield will be 102 bushels per acre, compared with the 126 expected under normal growing conditions. Similar reports come from other midwestern corn and soybean centers.

* In Georgia, the No. 1 poultry state in the nation, the drought is double trouble. In one week of July, high temperatures killed 350,000 broilers and 14,000 breeder hens. Higher prices for corn and soybeans, staples of chickenfeed, will mean higher prices at the supermarket.

* Officials in Pennsylvania say farmers there have suffered $500 million in heat-related losses, with the southeastern corner of the state described as undergoing one of its worst weather streaks "in a long time."

* Intense heat and dryness have plagued farmers in 27 west Texas counties, where state agriculture commissioner Jim Hightower, plugging for federal disaster relief, says, "We've got the makings of a new Dust Bowl out there."

* And to make the story thoroughly perverse, excessive spring rains and flooding in the Mississippi Delta and continuing cool weather--that is, hot but not hot enough--in California's Central Valley have cut into U.S. cotton production prospects.

Throughout the major midwestern corn and soybean states last week, government and university agricultural officials were agreeing that the damage to corn is considerable, but that soybeans can be salvaged if rain comes soon.

Elvin Taylor of Iowa State University in Ames said, "There's a rule of thumb that you can stomp all over your soybeans, but treat them right in August and you'll get a crop. The National Weather Service sees continued stress in our critical areas. We expect the problem to be with us."

Taylor said ISU crop data last week indicated that one-tenth of the state has lost between 30 and 50 percent of its corn crop, with counties in the southern half of the state suffering losses in the 30 percent range. "We expect everything to be down from 20 to 25 percent," he said.

In neighboring Missouri, USDA crop analyst D.M. Bay said July rainfall generally was three inches below normal, which, in combination with high temperatures, put corn and soybeans under heavy stress. "It's still not too late--a good rain would help soybeans and sorghum," Bay said.

"We're in a critical period," said USDA's E.L. Park in Indiana. "For corn, the question is: will the kernel develop? When the plant is under stress, it will preserve itself by slowing kernel development . . . . But until you can see the kernels fill the ear or abort, you really don't know what your crop is."

The pork and poultry industries are keeping a close watch on the weather, as well. Abit Massey, executive director of the Georgia Poultry Federation, said that chicken, turkey and egg prices are certain to go up because of the rapidly changing grain market.

"The PIK program and the opening of the farmers' reserve have already had a price impact on our industry," Massey said. "And that is aside from whatever the weather may do to corn and soybean prices. It's all going to add substantially to our costs."

In Des Moines, Orville Sweet, executive vice president of the National Pork Producers Council, said he sees no immediate impact on red meat prices. But, he added, "If there is a short corn crop, we could see supply affected with higher pork prices toward the last half of next year . . . . We're just one good rain away from prosperity."

Amen, might have said Mississippi Delta farmer Edgar M. Hood III, who's trying to raise 725 acres of soybeans in Tunica County.

Hood surveyed his crop at lunchtime Friday, with the temperature in the mid-90s, and pronounced it "burned up." He added, "We're starting to hurt around here. Most everyone irrigates to supplement the rain. My problem is that I've got the capacity to irrigate, but I don't have the money to pay for it. I don't know what we'll do."