Drain the tomatoes into a bowl, reserving the liquid and tomatoes separately.
Combine tomato liquid, white wine, garlic and rosemary in a medium saucepan, and bring to a boil over medium heat. Reduce the heat to low. Toss cubed brie with corn starch, coating well, and then add to the simmering liquid, one handful of cheese at a time. Whisk frequently, until mixture is smooth, then add the next handful of cheese, until all of the cheese has been incorporated. Stir in the reserved tomatoes.
Transfer to a fondue pot set over a small flame and serve immediately with dippers. If a fondue pot is unavailable, transfer to a heavy earthenware bowl that has been warmed slightly in the oven.