The temperatures can be downright cold at night in May and June, certainly below freezing above 10,000'. We experienced teens at Trail Crest mid-May and 20s at Chicken Spring Lake in early June.
Although, there has not been much snow this year, the north side sun protected areas will still be an issue. The only area I would not want to deal with if there was snow on this trip was the south side of Forester Pass, which I do not believe will be a problem this year in your time frame.
I agree with Harvey on footwear. There maybe enough snow that the traction you get from boots may will be worth the extra weight.
