Peel beets, sweet potato and potato. Cut each in half. In 3 or 4 batches, place vegetables through food processor for a coarse grate (you can also grate coarsely by hand).
Place mixture in a large bowl. Add eggs, flour, thyme and salt.
Heat around 1/4 cup vegetable oil in a large sauté pan over medium-high heat. Form bite-size mounds of latkes, taking care not to squeeze too much liquid out of the latkes. Fry until brown and crispy on each side, then place on a wire rack on top of a baking sheet to cool. Immediately sprinkle with an additional pinch of salt while they are still hot.
Serve warm with applesauce, if desired.