If I recall; it has been posted that the best method for heat is not more ventilation, but instead to insulate. Insulation protects from heat just as well as it protects from cold.
True, insulation tops have been discussed here before. I have also used these as well (2 inch insulation to be precise). I have discussed that very thing here with my results as well, and recently. I had a drawback. Perhaps not enough to be concerned with but I thought I might try something a lifetime beekeeper from my area has recommended. I did not know if others here might have attempted the vented top as well, so I decided to start this topic.
As a (newer) beekeeper, fourth summer, I like to experiment with different ideas and suggestions which seem reasonable and then weigh the results, then deciding which works best for me in my area. Vented tops have been recommended to me as a valid avenue for releasing heat in a over-bearded overheated hive here in the South. Not being one to be stuck in one mode but attempting to be open minded when reasonable, I thought I would try the vented option as described this season. I recently did so. I am happy to report it has proven to work "very well" in my location.
Always a threat in summer, Small Hive Beetles in my location are not to be taken lightly as noted. That is why I ask the question; Should screen tops be added when wedging, (venting), the hive top. Should the two be used together, is why I started this topic. Your input is very valued Mr Honeypump. Vented tops in my area work. Do these have to be screened because of SHB is the question. Hopefully I will find more answers concerning the two. I can always go back to insulated if I find insulated works best for me. I bet you are thankful that you do not have to deal with these awful pest; SHB ... Rough customers at times.