This thread prompted me to look through some pictures of my trip to India. At the Taj Mahal I was wearing shorts and a t-shirt. I recall that at a few temples they required more than shorts, but they had a wrap for your legs. I might have worn jeans one day, but definitely regretted it.
The temperatures when I was there (mid-September) were very warm and very humid (and very crowded practically everywhere). Well Jaipur wasn't as humid, but it was even warmer than New Delhi or Agra (similar climate as Phoenix I'd say).
For touring, I'd recommending dressing for comfort.