Place the strawberries in a small saucepan with sugar and thyme sprigs. Bring to a steady boil and cook until strawberries and liquid are thickened and coat the back of a spoon (about 30 minutes). Remove thyme springs and stir in balsamic vinegar. Let cool.
Preheat grill to medium high heat, about 400 degrees. Brush baguette slices lightly with olive oil and grill until golden and crisp.
When the crostini cool, spread with yogurt and a dollop of balsamic strawberries.