In a 3-quart saucepan, stir preserves and barbecue sauce. Diagonally cut hot dogs into 3/4-inch pieces, add to saucepan. Stirring over medium heat, bring to a boil and simmer until meat pieces are plumped. Remove from heat.
In a small bowl, stir water into cornstarch until smooth. Stir into hot mixture. Return to heat and boil for 1 to 2 minutes or until thickened.
Transfer to a serving dish. Serve hot with toothpicks.