Place grapes directly on the grates, or in a vented metal basket. Add to smoker and smoke for 15-20 minutes, covered.
For the goat cheese fondue, preheat oven to 350 degrees Fahrenheit.
Combine all ingredients in a small mixing bowl, whipping gently with a whisk.
Add whipped goat cheese mixture to a small, oven safe dish. Bake for 5-10 minutes until warm. Do not over-bake, as the goat cheese can begin to separate.
Serve the goat cheese fondue hot with room temperature smoked grapes for dipping.