Any flexing is going to generate more heat than a theoretical non-flexing frame would. You could probably calculate the difference if you had enough data, but never measure it. It's an interesting thought experiment, but probably has no real world practical use unless the frame in question is so comicly flexible that it has physiological affects.

So if you are using a non-optimally stiff frame, you are contributing more to the heat death of the universe than you need to be. The universe wants its tiny fraction of a second back.