You don't need a screen top. That would just let out too much of the humidity. just a few holes in the tub. Most people use a heat tape like flexwatt with a thermostat, or you can use a reptile heat pad with a thermostat, placed on the outside of the tub.
Sort of like this....
--------------------------------- tub top
\. . . . . . . . . . . . . . . . . . . . . / tub with holes (more holes shown to space out drawing)
-\. . . . . . . . . . . . . . . . . . . ./
--\[water]___________[hide] /
[table/floor/shelf] ---------- heat spot
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