Authorities suspect the cause of death was accidental carbon monoxide poisoning.
The victim's were identified as 44-year-old Darryl Jackson and Nadine Teamer said to be in her 30s.
The truck was inside Jackson's garage.
Family members said the two had apparently fallen asleep in the SUV some time Monday evening before Jackson was to report for work at a night club in Hammond, Ind. They said the couple apparently got cold and decided to turn the vehicle's heater on, not realizing the garage door was shut.
Jackson's family would not allow him to have his girlfriend stay over, and he sometimes slept in the sport-utility vehicle in the garage.
Jackson was the father of three children.
The Associated Press contributed to this report.
