Harris has told police he was supposed to drive his son to day care the morning of June 18 but drove to work without realizing that his son was strapped into a car seat in the back.
Harris was exchanging nude photos with several women, including teenagers, even on the day his son died when he was at work, Stoddard said.
However, defense attorney Maddox Kilgore said that evidence had no bearing on Harris' intent.
"I think the real purpose of all that is to publicly shame him," Kilgore said
In the weeks before the boy's death, the man also had looked at a website that advocated against having children and had done an Internet search for "how to survive in prison," the detective said.
"I think the evidence now is showing intent," Stoddard said. He said Harris should remain in jail because he is a flight risk: There is evidence he was leading a double life, he has family in Alabama, and the former 911 dispatcher has law enforcement experience.
Harris is a native of Tuscaloosa, Alabama, and moved to Georgia in 2012 to work for Home Depot.
The detective said after the boy died, Harris showed no emotion while being interviewed by investigators. At one point after Harris pulled over with the dead child in a strip mall parking lot, an officer told Harris to get off his cellphone, Stoddard said. Harris twice refused, using profanity, and was then arrested.
Scores of reporters and some curious members of the public were at the hearing just outside Atlanta, where police and prosecutors laid out the most detailed account yet of their case against Harris. Some of Harris' supporters also were in the courtroom.
Stoddard also described Harris' account of what happened that morning. Harris portrayed himself to investigators as a doting father who always kissed his son when he strapped him into the car seat because "he wanted Cooper to know his daddy loves him," the detective said.
Harris told police he had watched cartoons in bed with the boy, then had breakfast with him at a Chick-fil-A restaurant. Harris said he forgot to drop the boy off at day care, instead driving straight to work.
Harris has said he did not realize the boy was still in the car until he left work. A defense witness testified that Harris appeared to be extremely upset after pulling into the parking lot, trying to do CPR on his son.
"He was saying, 'Oh my God, oh my God, my son is dead, oh my god,'" witness Leonard Madden said.
Alex Hall, a friend of Harris since their sophomore year of college and a co-worker at Home Depot, said Harris talked about how much he loved his son all the time. He said he, another co-worker and Harris had gone to lunch the day the boy died and had planned to go to the movies after work that day.
"Nothing stuck out," he said. "Nothing was weird."