Harris, 33, has pleaded not guilty to charges of murder and second-degree child cruelty after he left Cooper for seven hours in the family's sweltering SUV while he went to work in Marietta, Georgia, on June 18.
According to a search warrant obtained by PEOPLE, after police seized computers and other electronic devices from his home, Harris "stated that he recently researched, through the internet, child deaths inside vehicles and what temperature it needs to be for that to occur," during an interview with officers. "Justin stated that he was fearful that this could happen."
He remains in jail without bond and is due to appear before a judge on Thursday.
Harris was not allowed to attend his son's funeral in Tuscaloosa, Alabama, on Saturday but he addressed the mourners via speakerphone, CNN reports. "Thank you for everything you've done for my boy," he said, noting that his son had a "good life" and he had no words to say. "Just horrible," he added. "I'm just sorry I can't be there."
Butch Dill / AP
Leanna was still on the phone with her husband as she followed her son's casket out of the church and said, "I love you," before hanging up.
Reporting by POLLY POWERS STRAMM