Care for Lawn of Creeping Thyme

This past winter we put in a "lawn" of creeping thyme. It is quite beautiful now, and I love the bees it attracts to my garden. I am wondering if I need to dead-head the flower stalks (I'm a rosarian)? How do I maintain the lawn?
I live in San Juan Capistrano, CA, USA, which is on the coast, half-way between San Diego and Los Angeles.

You might want to run the lawn mower over the thyme once it has finished flowering, set just low enough to cut off the most bothersome dead flower heads.
How to grow it: water when there is a drought. Pull out weeds before they have a chance to crowd out the thyme. Once the thyme is thick, not too many weeds will get a chance to germinate, but some will always manage it. In our area, clover and dandelions are the worst culprits.