In time, the flowers always die. If the leaves look fine, the hydrangea is probably fine too. Just trim off the brown flowers.

See the link below for pruning and deadheading instructions. Normally, by July-August, hydrangeas develop invisible flower buds for the Spring 2015 season. However, I suspect your plant was made to bloom this late by the wholesaler so this flower buds development business may be "off" compared to normal. Still, it is good info so you do not accidentally prune off flower buds. See the section on deadheading titled REMOVING OLD BLOOMS.

The flowers are going to be sensitive to sunlight or lack of water and, if they get brown, like rith_mi said, just deadhead them. The shrubs prefer morning sun and shade starting around 12pm or thereabouts. Bright shade all day also works. I suggest you add 3-4" of mulch up to the drip line. This will conserve water and protect the roots from heat and cold. The leaves should dry out in the Fall. If you notice that the edges of the leaves are turning brown from the edges inwards, it needs more water; you can apply 1 gallon per watering but apply it to the soil early in the mornings, not to the leaves so that does cause powery mildew issues.

Mophead hydrangeas like yours may not be winter hardy to very cold zones but it is hard to tell since the seller does not provide winter hardiness information. Usually Z6-ish is the limit.

Here is a link that might be useful: Pruning hydrangeas