In a small skillet over medium heat, add blackberries, lemon juice, honey and salt. Bring to a simmer and cook for 5-6 minutes, breaking up the berries with a potato masher or a fork.
Remove from heat and stir in lemon zest and thyme. Cover and refrigerate for about 20 minutes, until slightly cooled.
Lay out a sheet of plastic wrap and spoon about 1/2 of the blackberry mixture onto the plastic wrap, about the same shape and size as the goat cheese log.
Place the goat cheese on top.
Spread the remaining blackberry mixture on top and wrap tightly in the plastic wrap.
Refrigerate for about an hour, or until ready to serve.
Serve with your favorite crackers or crostini.