Rinse dried porcini to remove any grit. Place porcini and wine in small saucepan. Bring to simmer over low heat; remove from heat. Let soak until soft, about 20 minutes. Using slotted spoon, transfer porcini to work surface and coarsely chop. Line strainer with damp paper towel; strain wine into small bowl and reserve.
Melt butter in heavy large skillet over medium-high heat. Add crimini and shiitakes. Sprinkle with salt and pepper and cook until brown, stirring occasionally, about 8 minutes. Add shallot and stir until soft, about 1 minute. Add chopped porcini and strained wine. Boil until almost dry, about 1 minute. Stir in thyme. Season to taste with salt and pepper. Cool.
Remove Brie from box, discarding lid and paper. Using sharp knife, cut top rind from Brie; discard. Return Brie to box. (Alternatively, stack two 12-inch rounds of foil and fold up around bottom and sides of Brie, crimping foil at edges, leaving top exposed.) Mound mushroom mixture atop Brie. DO AHEAD Can be made 8 hours ahead. Cover and chill. Bring to room temperature before continuing.
Preheat oven to 350°F. Place Brie with mushrooms on rimmed baking sheet. Bake until cheese begins to melt and mushrooms are warmed through, about 15 minutes.
Serve hot with baguette slices.