If your thatch problem is really bad, a September trip may be a good idea. If you are going to overseed for the winter it's a good idea.
However, the more typical time would be a trip over in mid-spring, immediately preceding summer green-up. De-thatch and then fertilize and lime as needed. Water in. This allows the roots to receive an optimum dose of fertilizer, water, and to warm up a little sooner. Recovery will be swifter, possibly more complete as well.
DISCLAIMER: I work as an agronomist with row crops, and am not equally verse on turf maintenance! Your results will vary, depending on climate, soil type, and species of grass.