Crippen, 26,while competing in the FINA Open Water 10-kilometer World Cup at Fujairah, east of Dubai. He failed to finish and was found in the water two hours later, organizers said.
CBS News correspondent Mark Phillips reports that the race organizers have been criticized for holding the event in temperatures higher than 80 degrees, and for not having enough boats out with the swimmers.
The winner of the race, Germany's Thomas Lurz, criticized both FINA and race organizers on Sunday. He said the temperatures were too hot for racing, that FINA's open water schedule was too grueling and that organizers should have done more to ensure swimmers were safe.
"What we know initially is that he exerted himself more than he could, that's what we know," said FINA President Julio Maglione of Uruguay, attending an International Olympic Committee conference in Acapulco, Mexico.
"Apart from the investigation, we are awaiting a report from our technical director who says that everything was normal according to the regulations," Maglione said. "The medical report said it was huge overexertion, that's what they told me.
"It must have caused him to collapse."
"If the water's too warm and too salty, your dehydration level goes up so much faster," said Richard Shoulberg, Crippen's former coach. "I love him... we had a cup of coffee after every morning practice."
Gunnar Werner of Sweden, a member of FINA's legal commission and a former FINA honorary member, has been selected to lead the investigation and was due to arrive at the race site late Sunday.
"When he finishes his inquiry we'll put out our position," FINA executive director Cornel Marculescu told The AP. "We understand that they have the medical report in Arabic and they will translate it to English and send it to us. Probably tomorrow we will have it in the office."
Race officials confirmed a medical report and autopsy has been completed.
FINA rules place no limit on how warm the water can be.
"This is usually the case at events in this area," Marculescu said. "For some athletes it's good and for some it's not. Our rules cover only cold water.
"It's very surprising and unpleasant. This is a swimmer with a lot of experience. He was a fantastic guy and he came from a big swimming family," Marculescu said. "We've never had something like that happen in our sport before. I'm sorry for him and his family."
Swimmers complained of the warm water temperatures but Ayman Saad, executive director of the UAE swimming association, played down heat as a factor, saying that the water temperature was 84 degrees Fahrenheit at the start of the race.
All safety measures were in place including lifeguards, boats and divers, Saad said, and that FINA had signed off on everything before the race started.
"We are sorry that the guy died but what can we do. This guy was tired and he pushed himself a lot," Saad said. "He went down 400 meters before the finish line."
Usually at open water races of this level, a boat follows the last swimmer on the course.
"What I think happened is that the swimmers were in various groups. This is what I heard," Marculescu said. "On the last feeding station the coach was talking to him. But I really don't know. We have to wait for the investigation and then we will come up with our position on this. Otherwise it's only speculation."
Lurz insisted temperatures must have been above 86 degrees and that several swimmers suffered due to the heat. He said he talked to many swimmers who complained of swollen limbs, water loss and said he saw several who had become confused following their race.
"The water was amazingly hot. For sure, it was more than 30 Degrees (Celsius)," Lurz said. "Nobody thought such things like yesterday could happen ... It shows it was really just too hot. It was not just one swimmer. There were many swimmers who had serious problems in the water."
Another German swimmer, Angela Maurer, who finished fourth in the women's category, said she thought the heat was to blame for Crippen's death.
"I think the heat for him was too much," Maurer said, adding that she "will never swim here in the future again."
As well as Crippen, three other swimmers - two U.S. women and one Brazilian - were taken to a local hospital. All were released by Monday. Their names have not been officially released but include Brazilian Allan Do Carmo and American Eva Fabian.
Lurz, a nine-time open water champion, said Crippen's death highlighted the need for changes within the World Cup circuit, including setting a maximum temperature and easing rules that require a swimmer to finish the final race to gain points crucial to moving up the ranking and earning prize money.
Lurz speculated it was probably Crippen's desire to finish the race which cost him his life.
"I'm sure he tried everything because he is a sportsman, he had a heart as (a) sportsman," Lurz said. "He would never give up."
Swimmers on Saturday complained of warmer than usual conditions and Fujairah police have opened an inquiry into Crippen's death. Crippen's former swimming coach, Shoulberg, said Crippen had told him in a recent telephone call that the water was 87 degrees.
Swimmers were the first to respond when Crippen failed to arrive at the finish. Several returned to the water to search for him and were soon followed by police and coast guard divers. Crippen's body was found just before the last buoy on the 2-kilometer triangular course, race organizers said.
"It was unacceptable that swimmers were searching for another swimmer. That is horrible," Lurz said. "Swimmers go under water in seconds. There need to be more boats, jet skis, canoes who can take care of every swimmer."
Lurz and Maurer blamed organizers for allegedly failing to provide enough boats to monitor the swimmers.
"There were not enough lifeguards and there were not enough boats," Maurer said. "There were no jet skis or boats leading the women. I never saw a leading boat. I never saw a rescue boat. I saw nothing."
Crippen was rushed to shore and transported to Fujairah Hospital, where he was pronounced dead.
"I can't even imagine how this could have happened to Fran," Crippen's teammate Alexander Meyer said.
Maglione said he was told that after eight kilometers Crippen told his coach that he wasn't feeling well.
"He continued and he was found in the deep of the water," Maglione said from Acapulco, Mexico, where he was attending Olympic meetings.
Swimming officials in the UAE canceled the 15km open water event which was scheduled to be held Wednesday at the same location, with swimmers having expressed concerns.
"We were not staying back for Wednesday's race anyway," said Ana Marcela Cunha, the overall champion in the women's competition.
The 10K race is the only open water discipline that is an Olympic event, having made its debut at the 2008 Beijing Games. FINA had been seeking to add more open water races to the Olympic program but with the IOC not intent on adding events Marculescu said the swimming body has now shifted its focus to adding more athletes to the 10K men's and women's Olympic races, which had 25 competitors each in Beijing.