Put the potatoes and turnips in a pot, cover with cold water, and add the thyme and 2 teaspoons salt. Bring to a boil and cook, uncovered, until soft, 20 to 25 minutes. Drain, then mash, adding cooking water if needed to thin the vegetables and the cheese and/or butter to taste. Taste for salt and season with pepper. Keep warm in a double boiler if you're not ready to serve.