Mom is a slow learner, but here is what I think eliminated the crying this time:
Making the water warm enough. I was so worried about getting it too hot that I was freezing the poor little guy. I finally got a thermometer.
Enough warm water so that most of him is submerged rather than out of the water being cold.
Put the soft but thin and flimsy baby towel inside a big fluffy towel, because what he really likes is to be bundled and warm rather than wet and cold.