For medium, cook filet mignon for 2 to 7 minutes -- until the meat reaches a temperature of at least 140 degrees. For a steak cooked medium-well, cook filet mignon for 4 to 9 minutes -- to a temperature of at least 150 degrees. Turn the filet mignon once about halfway through the cooking time. Remove the filet mignon from the oven and place it on a carving board. Cover the meat loosely with aluminum foil, then allow it to rest for 5 to 10 minutes. Carve the meat, and then transfer it to a warm serving platter.