RE: "what the average temperature runs at that time of year? I'd also like to know in a ruff estimate the number of people I might encounter", it can vary but highs in the afternoon should be more like 100-105, maybe an occasional 110 in mid-May.
There won't be many people, like 5 or less at the Palm Spring. Not sure how many at the Lower Spring. You might even have the Palm Spring to yourself for a few days.
I can tell you it's spectacular to be there by yourself. It's a big, big, hot place and it's special. Most of my trips are in the summer these days, though I used to go every Christmas for 10 days or so. The count on Y2k was estimated at 600 and that's not really my cup of tea.
All the usual warnings about preparation, carrying lots of water and having a reliable vehicle apply even more in the summer.