Prepare apples by gently scrubbing them with the rough side of a clean sponge. Place on a towel to air dry. Put on a small tray and place uncovered in the refrigerator for at least two hours. When ready to use, remove stems and place a stick through the top of each apple into the flesh.
Bring cream, butter, and salt to a boil in a small saucepan. Remove from heat and set aside.
Boil sugar, corn syrup, and water in a 3- to 4-quart heavy saucepan, stirring until sugar is dissolved. Boil, without stirring but gently swirling pan, until mixture is a light golden caramel color.
Carefully stir in cream mixture (mixture will bubble up) and simmer, stirring frequently, until caramel registers 248°F on thermometer, 10 to 15 minutes.
Pour into a small diameter pan, deep enough to hold the caramel with enough room for dipping.
Dip cold apples into caramel, allow excess to drip off and place on a parchment lined tray. Allow to sit for two hours for the caramel to set up.