Combine 1/2 cup sugar and 1/2 cup water in a medium saucepan and cook over medium heat until the sugar dissolves, about 4 minutes. Add the jalapeno and thyme and let it infuse for 5 minutes. Remove the jalapeno and thyme and set aside.
Pour the simple syrup and chopped watermelon into a blender. Blend until very smooth, about 2 minutes. Serve cold over ice and garnish with the sugary sprigs of thyme.