Beat the butter until smooth and set aside.
Meanwhile, boil the suagr mixture until it reaches 248 to 250 degrees on the candy thermometer. Do not let the temperature go above 250 degrees. Turn off the heat and immediately pour the mixture into a glass measuring cup to stop the sugar from cooking. Pour a little of the sugar mixture onto the egg whites and beat them on low. Slowly add the rest of the sugar and then beat on high for 2 minutes. Beat on low until the mixture is cool. Add the butter, 1 tablespoon at a time, to the egg white mixture, beating continuously on low until all the butter is added. If the mixture starts to separate