Nicholacci;
I hiked Whitney in 2011(record snow year) in late August and there was still 3 feet of snow in many sections. I've day-hiked Whitney every August since 2004 and have experienced all sorts of conditions even so late in the season. Going in June this year will require Mountaineering experience with record snow depth(worse than 2011) and dangerous creek crossings(though not many). Not too far away, Mammoth Summit has received 66 feet of snow with more to come. This year will be an all-time snow record with catastrophic flooding. I would personally wait until September/October time frame. There are many other majestic hikes in the Sierra's. Whatever you decide, have fun and be safe. note: Steve C-/Bob P and Wandering Jim and many others: thank you for all the informational posts. They can save ones life.
