In a medium, heavy-bottomed saucepan over medium heat, combine the sugar and zest (from the 1st step) with 1 cup water. Whisk the mixture until the sugar is dissolved, and bring the mixture to a boil. Let boil for 1 minute before removing from heat and transferring to a wire rack to cool completely. After about a minute on the wire rack, add 2 to 3 sprigs of fresh thyme and whisk gently into the mixture. Let sit for 30 minutes.