First, heat the oil in a medium-size heavy skillet over medium-high heat. Then, add the mushrooms, shallot, and thyme and sauté until the mushrooms begin to soften (about 2 minutes).
Next, place the flour in a large bowl. Cut the rind from your Brie and discard it. Cut the Brie into cubes and drop into the flour. Toss the cubes to coat, separating the cheese cubes.
Crumble the Roquefort into the same bowl and also toss to coat.
Pour the wine into a medium-size heavy saucepan and bring to a slow simmer over medium heat. At this point, add the cheese by handfuls, slowly, and stirring all the while until each addition of cheese is melted. Keep stirring until the Brie fondue mixture is smooth.
Next stir in the mushroom mixture into the fondue. Season with generous amount of pepper and transfer it all to a fondue pot.
Set the fondue pot over a candle or a canned heat burner. Or if you have an electric fondue pot, make sure you are familiar with the settings before using it. Serve with bread and vegetables (see below).