In a large pitcher, pour in water and add in the tea bags and thyme. Cover and place tea in the sun for about 4 to 5 hours to steep.
Using a muddler, or a wooden spoon, mash 1 cup of the strawberries to release the juice. Combine with the remaining strawberries, cover, and set in the refrigerator until the sun tea is done.
Stir the tea with a wooden spoon and add in the strawberries and sugar, if desired. Serve over ice and enjoy!