Ok, as long as you done have any other router connected to the Arris modem/router, you'll be fine.
Ya, its a pain getting wired installed in a pre-existing house. I had to craw up in to the attic of the old house to get wired ran to that end of the house. Was fairly easy when we did the new addition. So glad we got CAT6a in though.
You should be good now. Just be sure that when installing CAT cable that the plug ends are tested well before closing everything up. Thats the one pain having to test the plug ends.
Ya I keep a laptop cooler under my main host router all the time. I know there is fans in the Hopper on the sides I believe. No vents under mine. I need to look into maybe some side fans for additional cooling. Mine sits on a well ventilated equipment rack.