Well, Amee is recommending several good things here, but for all the wrong reasons.
She is correct to recommend a location with little or no direct sunlight. This is because direct sunlight will increase the temperature of the piano very quickly relative to its ability to adapt, and at the same time dramatically decrease the relative humidity. Since the sun goes up and down every day, a daily regimen of sudden temperature and humidity changes like this will kill your piano.
If you have hardwood floors, a rug under the grand is one mechanism to dampen the acoustics, NOT because of scratches. Our grand is on caster cups that are made for such applications, and no problem. My piano teacher's two pianos are both on hardwood floors, with little rugs just under each bench. She has drapes on the walls, adn prefers this type of live environment. Much of the piano's sound comes out the bottom.
I would not recommend putting a blanket over your piano to play it.
Mindy