You should cook a 2 pound eye of round roast in an oven for about  an hour and fifteen minutes at 325 degrees Fahrenheit for rare. When tested with a meat thermometer, the â¦ meata??meatÃ¢ s  internal temperature should read 140 Degrees. fahrenheitou should cook a 2 pound eye of round roast in an oven for about  an hour and fifteen minutes at 325 degrees Fahrenheit for rare.