Combine sugar and flour in a heavy saucepan; whisk in vinegar and 1/4 cup water. Bring to a boil over medium heat, and boil, whisking constantly, 1 minute or until thickened. Remove from heat; stir in salt and butter.
Stir beets into sugar mixture, and cook over low heat 5 minutes or until thoroughly heated, stirring often. Serve immediately. Or let cool, and spoon beet mixture into an airtight container; chill 8 hours.