A Raleigh resident said he discovered the body when he was in the area to clean up trash: "I was shaking."
Durham officials said each park will get a risk-based action plan, but for now, the closures stretch on.
The Pullen Aquatic Center, Pullen Community Center, and tennis courts will remain open.
The high-tech building more than doubles the academy's size, creating room for more sports, more kids, and more programs such as camps and leagues.
It happened Tuesday at Church Street Park, where burn marks remain visible on the grass.
In the past dozen years, 18 projects have been funded, totaling $21.12 million, including $1 million to Ting Park in 2013.