I would think the best thing you could do is drill a few 1” diameter holes near the top and bottom of the compartment to allow the hot air a place to escape, and cool air a place to enter. If you have a Cargo hold next to the WH, dump the heat into their.
I might suggest a thin sheet of pink foam, ideally foil faced, under the dinnet bench access lid. But honestly, if the 3-4 inches of cusions is to warm, I do not see how a little more insualtion would help. But it might.
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