I install windows for a living, if we lay a window on the grass on a hot day with the sun shining threw it for verry long (1-2 hrs)it will burn a pretty square in there lawn an almost kill the grass under it.
Some glass has UV protection like spf 50 windows, an it dosent get as hot, But i still think it would be to much.
Use plastic corrigated pannels made for green houses. It shines light in at any angle an u just use it for the lid. Any glass shop can get em or check out the net.
Also use a thermostat to start fans automaticaly when the temps get to high.