SOFIA, BULGARIA, JAN. 19 -- Dozens of enterprises and tens of thousands of apartments in this fuel-starved country's second biggest city were without heat today, an official said.

The critical situation in Plovdiv, with a population of 370,000, reflects the nationwide energy shortage caused by sharply reduced Soviet crude oil supplies, the Persian Gulf crisis and a lack of hard currency.

Although the situation appeared most serious in Plovdiv, other cities have reported major energy problems in recent months. Some have been forced to ration electricity.

Deputy Prime Minister Dimitar Ludzhev said that next week, the government will issue a decree permitting establishment of a network of about 20 privately run gasoline stations to supply fuel that has been virtually unavailable nationwide for weeks. Those stations would be supplied with gasoline from Western companies with the help of private businessmen in Bulgaria.

Petar Petrov, an operator at a heating plant in Plovdiv, said today that on Friday, the plant had only about 500 tons of oil, enough for one day of operation.

Speaking by telephone, he said the plant was still working today, but that heat in all apartments had been cut off in the district and that only hospitals and schools were normally heated. He said 30,660 apartments had been unheated since Friday.

Plovdiv plant managers described the crisis in a telex message to Prime Minister Dimitar Popov, the state-run Petrol distributor of gasoline and fuel oil, and other agencies, Petrov said.

The message said that since winter started, 30 enterprises in Plovdiv have not been heated at all for lack of fuel oil and others have received only limited amounts of heat needed for production. This meant that practically all industrial plants in the Plovdiv area, 100 miles south of Sofia, have been affected.

Ludzhev said the government has been seeking heating oil from Turkey. But he cited problems in obtaining the necessary credits from a Turkish bank.