Our network now works not because of the heat breaking, but because I swapped our main SMC router for a LinkSys router which Bluegrass Mama surplussed when I fixed her wireless router. Those SMC routers have history of toasting on me, this may the third or fourth one that flaked out on me.
All this means I only have one spare working router, although I could change things around so that the WiFI router carries more than just our limited WiFi traffic. (What? You don't have a distinct WiFI network, or any spare routers?)