Final answer:
The recommended internal temperature for cooking a beef filet varies depending on the level of doneness desired, with temperatures ranging from 125°F for rare to 160°F for well-done. A meat thermometer should be used to accurately measure the internal temperature.
Step-by-step explanation:
The recommended cooking temperature for a filet, specifically beef filet mignon, should reach an internal temperature that matches the desired level of doneness. Common benchmarks for doneness are as follows: 125°F for rare, 135°F for medium-rare, 145°F for medium, 150°F for medium-well, and 160°F for well-done. Using a reliable meat thermometer is crucial to measuring the internal temperature of the meat accurately.
It is also important to note that meat continues to cook after it has been removed from the heat source, a phenomenon known as carryover cooking. Therefore, it's often recommended to remove the filet from the heat when it is a few degrees below the target temperature, allowing it to rise to the perfect temperature while resting.