Thatch is the accumulation of dead and decomposing turf stems, leaves and roots intermixed with live plant roots. Clippings do not contribute to thatch buildup. Clippings decompose quickly and should be returned to the turf. Thatch is the brown layer between the soil surface and the green top growth. A thatch layer of approximately 1/2 inch is beneficial because it acts as a buffer at the soil surface and protects the plants from weather extremes. Thatch that builds up over 1 inch, however, can inhibit water and air movement and eventually weakens the turf stand. What is your thatch thickness?

Cool season turf is growing best in May and September and good detaching is injurious to turf so early in those months is the best time as the turf will have time to recover.  September is preferred over May as the season doesn't go into a hot/dry summer.  

Core aeration is a good way to reduce thatch that is not too thick because it removes plugs of thatch and soil to the lawn surface where they decompose and distribute soil & microbes on top of the thatch as well as allow air and water through the thatch to the turf roots.  It's also less injurious to turf than mechanical dethaching taking turf about 15 days to recover.

Core Aeration & Dethatching of Lawns-MSU

Managing Thatch In Home lawns-ILL

How to Control Thatch in the Lawn-UMN

Managing Thatch in Lawns-PSU

https://extension.psu.edu/lawn-management-through-the-seasons

In answer to your question early May or early September would be the best times to dethatch.