Grammy-winning singer Natalie Cole died of heart failure caused by a rare lung disease, her family said Thursday. 

Cole, the daughter of the late singer Nat "King" Cole, died Dec. 31 at a Los Angeles hospital. She was 65 years old and had battled drug problems and hepatitis that forced her to undergo a kidney transplant in May 2009.

Cole's family said in a statement to The Associated Press that after the transplant, she was diagnosed with pulmonary arterial hypertension, which causes shortness of breath, dizziness and sometimes chest pain. Because Cole's case was idiopathic, the exact cause is unknown.

"[Cole] responded well to pulmonary arterial hypertension-specific agents over many years, during which she performed many concerts world-wide, but eventually succumbed to intractable right heart failure, an outcome that unfortunately commonly occurs in this progressive disorder," the family's statement read in part.

Cole is best known for her her 1991 album, "Unforgettable ... With Love," which paid tribute to her father with reworked versions of some of his best-known songs, including "That Sunday That Summer," ''Too Young" and "Mona Lisa." The album sold an estimated 14 million copies and won six Grammy Awards, including album, record and song of the year.

in her 2000 autobiography, "Angel on My Shoulder," Cole discussed how she had battled heroin, crack cocaine and alcohol addiction for many years. She spent six months in rehab in 1983 and blamed her 2008 hepatitis C diagnosis on her past intravenous drug use.

The Associated Press contributed to this report.