Boozy Peach Lemonade

Pretty Peach Lemonade - 2 ounces peach flavored vodka such as Absolut, A Peach, 1 1/2 cups sugar, 1 cup hot water, 2 1/2 cups fresh squeezed lemon juice, 1 cup fresh peach juice or puree, 3/4 gallon cold water, thyme to garnish