The small buds would never have become large enough to bloom and the plant aborted them when it became warmer. Depending on how warm your temperatures have been the larger bud also appears to have been effected by the heat.

Your peonies are simply done blooming for the year. It's perfectly normal for the smaller buds to not open. Some folks even remove the secondary buds when they are tiny, so the plant puts all its energy into the big primary blooms. Your peonies look happy and healthy, so you have something to look forward to next spring.

I agree 100% with Festiva. It is normal for Peonies.

Thank you everyone! They were certainly beautiful while blooming.