For a short time, say 2 or 3 hours, I would use a cooler or ice chest. No ice or ice packs are needed. The temperature rise in a hot car should not be very much if its a decent insulated ice chest. The concern with using ice packs would be the humidity and perhaps condensation.
I would not leave this camera/ice chest in a hot car all day. Either travel light or have a companion to baby/camera sit with the windows open is the best alternative.