Yury,
I normally try and hike in the area some time during the 2 weeks before and after Labor Day. Though the days are a bit shorter than in mid-summer, but the weather is more stable, the mosquitoes are basically gone, and it's not nearly as hot (I just hiked the area in late July this year -- an departure from normal for me -- and because of the heat and mosquitoes, will probably not repeat that again, but will return to late Aug/early Sept in the future). Also after Labor Day, it is generally less crowded, not that being crowded is a big problem on Whitney, given the quotas.
So echoing the previous post, I would highly recommend the two weeks before and after Labor Day -- my favorite time in the area.
CaT