Get some GLAD Press N Seal (not plain plastic wrap) and stick it to the screen, leave opposite corners open for ventilation. You should have a UTH so an overhead light isn't needed to keep the temperature at the appropriate levels.
What kind of substrate are you using? We've found that cypress mulch is ideal for maintaining humidity. Make sure you get the stuff designed for reptile enclosures, the mulch from garden centers may be a mix of different woods, or it may contain pesticides.