I know of no product that will withstand heat well enough other than 'muffler cement' and that isn't really glue.
I would cut two steel (preferably 'stainless' if you can find it) plates of the same dimensions, drill both and mount one in front, the other inside, and rivet at the corners through the rusted partition.
You can buy an inexpensive 'blind' riveting tool (normally in a kit) at most hardware stores.
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