I have two heating lamps, one for daytime and a red one for night. My concern is lately it has been getting pretty hot, like 90 F (32 C), and I'm worried having the light on will make the cage too hot. At the same time I don't want to leave him in the dark all day since the cage isn't near the window.

Also sometimes I take him for walks in Central Park. Do you think this is a bad idea? He seems to enjoy rolling around in the grass for an hour or so a week, but I don't want him to get sick or anything.