Preheat oven to 425°F. Place a baking sheet in the oven while it preheats.
Roll out the dough on a sheet of parchment paper. Sprinkle fontina on dough, leaving a 2-inch border around the edge. Drain the cherry tomatoes, saving the liquid. Arrange the tomatoes over the cheese. Sprinkle with feta and thyme. Fold dough border over the topping, pleating the edges as you go. Brush edges of dough with the liquid from the tomatoes. (Reserve the remaining liquid to use for cooking or salad dressing—it has lots of flavor!).
Remove preheated baking sheet from oven, and carefully transfer the tart to the baking sheet. Bake 20 minutes, or until the crust is golden, and the filling is bubbly. Let stand 10 minutes before slicing and serving.