Cooking meat is simple as long as you have the touch. Most professional chefs can use their finger to test the wellness of meat. Especially when it comes to filet as there is no tissue and it is all tender beef.
I used the Fluke thermocouple and stopped at 45°C, and let is rest as it finished at 48°C. This was a good result if you like it medium rare, and rare would be nearer 42°C.
I seared the Chateaubriand when it was cold 5°C in order to maintain the juices. From practice, I often sear the meat in advance, coloring it and letting rest before I cook it. This locks in the juices.
I never let it touch the pan, (suspend it) as it will burn on one side. I start low 60°C and finish at 80°C with a core temperature of 45°C. The seasoning is done at the last-minute prior to serving, and yes I wrapped it with bacon to keep it classical and tasty.