I skimmed his page, and while I don't want to say C2C is a walk in the park, if you're a regular hiker, start early (4AM isn't too early), eat & hydrate regularly, most make it fine. Keeping in mind that Palm Springs is about 500', and the tram is 8400', the goal is to get part way up by mid-morning so you're not caught low in the heat. But, it's not an epic. If you live or have access to the mountains in the East, a Presi traverse, a Pemi loop, or the Devil's backbone, or the Great Range traverse are much more demanding.
Most people (in my experience) take the Palm Springs tram down. Getting back to the museum is a pain as it's 7 miles away. I've either 1) hitched a ride with other hikers who gave me lift or 2) taken a cab and sometimes shared the fare. A few people continue on 5.5 miles to the summit. A few turn around at the tram and hike back down to the museum.
In my experience, one of the toughest aspects of going from a temperate climate to an exceptionally arid one like Palm Springs (maybe 5% humidity mid-day?) is acclimatization, and not so much to altitude. Most of us acclimate to altitude faster than adjusting to the extremely dry temps. I don't know if the local SAR unit (Riverside County) still does it, but around 2007 or so they started to stash water in emergency caches as dehydration was a major cause for rescues. What works for me on this hike is to super hydrate before starting, and lug a 100oz bladder of water. If memory serves, NYKer has posted about other hikes he's done in the West, so I doubt he needs the advice re: hydration.
Oh, before I forgot - the tram station has some mighty fine cold beer. Not too many hikes have a cold adult beverage available up top, at least one you didn't lug yourself.