The Mt Whitney Weather page (link to the left) has a line, "Cottonwood Lakes, elev. 10150' 7-day Temperatures".
If you check that one, or
this 28-day link, you can get a pretty good idea of what to expect at the 10,000' elevation: Lows ranged from 26 to 40 F.
Checking NOAA and other sites, it appears the lows will be around 35 even at the summit this weekend.