The small size of Calimyrna figs makes them perfect for serving. If you can only find larger figs, simply halve them and stuff accordingly.
In microwave-safe dish, combine figs, sugar, water, and red wine. Heat in microwave oven 5 or 6 minutes at 80% power. Remove; let figs steep and cool 10 minutes, then drain, discarding liquid. Meanwhile, mix goat and mascarpone cheeses in a medium bowl. Mince half of the thyme leaves; add to cheese mixture. Set aside remaining leaves. When figs are done steeping, create a small hollow in each with your thumb; pipe in cheese mixture or stuff using the concave side of a teaspoon. Garnish with remaining thyme leaves.