You can get some idea about the weather a day or two before by looking at reports for surrounding areas but that will only be marginally accurate when applied to Whitney. I've been surprised often.
It can get windy or cold but afternoon thunderstorms are the most common phenomenon. Seems like you can almost set your watch by them and July is especially bad. They usually form up in the afternoon and around 2pm or so do their thing (lightening, rain, and hail) and evaporate as evening sets in. The best bet is to get an early start. For July I usually just pack a light sweater and a rain shell. It usually starts raining up top first and often doesn't make it down to the valley. Once the storm starts to let loose you'll be forced to descend. It's not uncommon to get rained on up higher and then get back down to the Portal only to find it dry down there.
It's also not a bad idea to carry an emergency poncho (the thin disposable ones), space blanket, and/or a trash bag.
-Rick