Michael,
Look to the left side of the web page, and you should see "Mt Whitney Weather". If you click on this link it will take you to a new page with several links to various weather sites. Check a few of them, and you will see that the temp atop Mt. Whitney will be in the 30's for most of the week, so dress warm. Nonetheless, this looks to be a great week for weather (after Today), with clear skies, no rain, and little wind.
As has been posted many times, this trail is well used. Even if you end up going alone you will see/meet many people on the trail.
John