Along with dethatching usually comes overseeding. The seeding is the important thing to time. It's a good time to put down more grass seed to fill in bare/thin spots now that you've opened up the soil. Ideally you want the soil temperature to be above 65 degF for cool season grasses.
It's going to depend on what type of grass you currently have and what type of grass seed you plan on putting down.
Perennial ryegrass is one of the quickest to establish.
Tall fescues and fine fescues are a little slower but fairly quick. 1-2 weeks you'll have full germination and the lawn will be pretty well established for winter in about 4 weeks total.
Kentucky bluegrass takes longer to fully germinate. Up to 4 weeks and then needs time to establish as well.
If your in Kansas City, KS it looks like you should have enough time to get perennial rye or fescue to establish before winter if you put it down soon. see http://www.weather.com/weather/monthly/USKS0298
Remember, the soil temperature usually stays warmer longer than air temperature.
You may not even need to dethatch. 1/2" of thatch is OK but it sounds like your lawn needs improvment and dethatching and overseeding will help improve the appearance. If you can spread a 1/4" layer of compost over the lawn when you put down the seed after you dethatch that will also help. You need about 1 cubic yard of screened compost per 1,000 sq ft of lawn. If you have a truck you can pick it up cheap or have it delivered in bulk. Spread it around in piles across the yard and use a rake to spread it out evenly across the lawn.It'll help keep the seeds moist too.