Thirty-six people were burned to death and numerous others have been seriously injured in fires resulting from rear-end collisions involving Toyota Corollas and Coronas made between 1966 and 1978, according to a Washington-based research group.

The Insurance Institute for Highway Safety, which first reported in 1973 the danger of fiery deaths when Ford Pintos are hit from behind, said that 17 persons died between 1966 and 1973 when their Toyota Coronas were rear-ended and that 19 persons burned to death between 1970 and 1978 when their Toyota Corollas were hit from behind.

William Haddon, president of the insurance institute, said, however, that the group's statistics are based on a collection of newspaper clippings, police and government reports and that no other data are available on the death and accident rates.

He added that other cars could have worse records than the Toyotas but that those kinds of statistics aren't kept by any government agency in one spot. The high numbers of fiery fatalities with the Toyotas in newspaper accounts caught the institute's attention Haddon explained.

The National Highway Traffic Safety Administration has been investigating the rear-end collisions with Toyotas since 1973, an agency spokesman said yesterday. The investigation was started following requests by the insurance institute, and no conclusions have been reached yet, the spokesman said.

A spokesman for Toyota Motor Sales U.S.A. Inc. said that the government agency already had cleared its cars in tests on 1969 to 1974 models. The tests showed no significant fuel leakage from the gas tanks when hit, the Toyota spokesman said.

The government spokesman said that 1973 Coronas and Corollas did pass a crash test but that the agency felt that further investigation was needed.

In addition, during an insurance institute crash test under labortory conditions, an American Motors Gremlin was driven into the back of a Toyota at less than 40 miles an hour, and the Toyota "spontaneously ignited," Haddon said. "The flames were swirling around the driver in less than a third of a second." Sitting in the driver's seat in this case was a test dummy, Haddon said.

Last year the insurance institute asked NHTSA to investigate Toyota fuel tanks and in a letter cited three deaths in the flaming crash of a 1973 Toyota Corona sedan near Fort Lauderdale.

The institute also said that the system used in the 1973 Corona sedan has the gas tank underneath the trunk with access to the filler pipe just above the center of the rear bumper. In two tests when the car was hit from behind, the filler pipe was bent forward sharply, the gas cap was torn off and gasoline was injected directly into the passenger compartment.

In its letter to the NHTSA, the institute said fuel-system problems in some Toyotas should be improved quickly "before more people are needlessly maimed and burned to death."