Thyme is a wood perennial. It will continue to grow each year spreading by putting down roots where the longer shoots reach new ground. I tend to thin mine pretty hard in the fall to get rid of the woodiest chunks so that new, tender growth occurs in the spring. Sort of like a controlled fire in the woods. I let mine flower, but some people cut them off. You can eat the flowers, but I don't get much taste out of mine.

Benign neglect is the secret to many perennial herbs. Tend them in fall and again in the spring and let them do what they want the rest of the year.