It depends on where you are and how hot it is now and how hot it will be soon, but I would be more likely to do it in the fall or in early spring before it starts putting out leaves. You will be less likely to lose as much bloom by timing the move carefully.

I prefer to move clematis in the fall or spring but have successfully moved them throughout the growing season. Be sure to dig wide and deep and keep as much soil on the root as possible. Also keep a watch on moisture levels.