The Emergency Medical Service said a man fell 70 feet from a tree in the park.
Sixty members of the city's Emergency Medical Services were also there.
The incident marks the second death within two months in which the Emergency Medical Service's response has been at issue.
The Emergency Medical Service reported taking 10 people to local hospitals, a figure that may have included the dead baby.
The Emergency Medical Services said 162 people had been treated at eight hospitals.
The heat also brought the highest number of calls to the city's Emergency Medical Services for any day so far this summer.
The call is then transferred to the Emergency Medical Service in another building.
It took the Emergency Medical Service 25 minutes to respond.
During the second world war, part of the hospital was taken over by the Emergency Medical Service for military use.
Emergency Medical Service and fire protection are provided by volunteer agencies.
