We did the same ride and direction last year in June. It was hot as hades! Heat wave. I looked at the route and picked out several towns and a week before started pulling the weather in those areas to give us a hint. We picked it just right. We only took light jackets and the wife wore hers one morning for about two hrs, other than that we were good. Good luck, it's an awesome ride.

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There are two things to aim at in life: First, to get what you want; and after that, to enjoy it. Only the wisest of mankind achieves the second.
Author unknown, but I like it!