Oh m'god, it did!
Two long but easy days put me at noon, Fri., in Silver City, NM., one of the cooler towns I've seen.
All morning I thought there was something wrong with the bike. Turned out it was just tired legs. Did need a new chain though and a batch of new tubes; had 6 flats in two days.
Now I head into mountains and desert and more long stretches between towns. About 700 miles to go.