get rid of the lid, you don;t need that... it will actually suffocate your plant from lack of fresh co2 unless it has holes in it or you remove it regularaly.

basically what you've already done is a good way to raise the humidity if it is really that low... just leave an open container of water in the grow box/room/whatever, several if you need to.

that being said... what are you growing in? totally drying out in 8 hours seems a little unlikely given your temps even in extremely dry climates.