If you have any type of ventilation at the top of the hive, you are just creating a draft up though the hive by having the bottom open. It will definitely be warm and easier for them to keep a larger brood patch with it closed. When I use to use screened bottom boards, I never opened them before Labor Day.
I know some will say leave them open all year round. But my experience has shown me that more brood will get raised earlier with them closed.