In a medium bowl, toss the Swiss and Gruyère cheeses with the cornstarch.
Smash the garlic clove, but leave it whole.
Add the cheese, wine, lemon juice, garlic, salt, and pepper to the slow cooker.
Cover, turn the slow cooker on high, and cook for 15 minutes. Remove the garlic and stir. Cover again and cook for 45 minutes more on high, stirring every 15 minutes, until the cheese is melted and smooth. Be careful not to overcook or the fondue will seize.
Turn the slow cooker to warm and serve the fondue with your favorite items for dipping.