At the time of the alleged kidnapping, when Wilson was taking the baby for a walk, it was 31C (87F).
Baby was wearing a onesie, which I understand is a short-sleeved t-shirt with snaps. There is no mention of a hat or any protection from the sun. Do people take their babies for walks at high noon on hot days?
http://www.timeanddate.com/weather/usa/indianapolis/historic
I thought WW said something about a cover for the baby. It's possible that cover was to protect Delano from the sun.
Although, I don't recall much more about the cover, and while it is possible it was to protect him from the sun, I don't believe that is why he had a cover.