Yes there are heaps of options. Generally you'll want to be climbing in the morning and later arvo/evening. Don't even bother with the hottest parts of the day.
Get up early and head for anything on the right side of central gully or pharos gully. There is also heaps of other morning shady options including castle crag, Mari buttress, watchtower chimney, and a few climbs in the bowels between bard buttress and tiger wall. One side of bushrangers is shady in the morning and there are heaps of other little gullies and spots that you can occupy yourself in.