Hi Greenhorn1
Hydrangeas are essentially shade lovers. Having said that the ideal conditions would be morning sun afternoon shade, They do not relish hot afternoon sun. If they are in sun a lot of the time then make sure the soil is kept really moist around the roots and a good mulch. Hope this helps.

Our hydrangeas do well in more or less full sun though.Perhaps pure white ones are more susceptible?
Try Phloxie's advice anyway.

They don't like full sun in the afternoon.
If you decide to move it, wait until it has lost its leaves. Make sure you have the whole root ball. Give the plant a good watering before you start digging (several gallons the night before and more avian in the early morning). Start close to the stems and carefully work outwards to uncover the rootball - add another 6" at least and then start to work down. When you know how big the rootball is your under-gardener will know how big a hole he needs to prepare while you dig out the plant (at least half as wide again and half as deep againas the rootball) Wrap the rootball (ideally in damp hessian - realistically in a bin liner or plastic tarp) and replant in the hole that your under gardener has prepared (you can be cup heckling the hole, adding a good layer of grit and organic material) while UG transports the plant.
Plant it at the same depth, back fill with lots of good organic material and grit. firm it down and give it another good drink. Make sure that it doesn't dry out while it's settling in - the grit will help to keep the soil well-drained - hydrangeas like that weird thing of moist, well-drained soil, ie they don't like standing in water (who does?)

Sure you're all right about the shade, but if its any encouragement I have four that get full sun all afternoon and they are all doing fine (one is taller than me and much wider...)