I not sure about the white wash- don't think it would make it look warmer though- if it were mine I would change the color on mantle and book shelves- they are solid white right?

Need a close-up picture of the tile next to the painted wood. But from what I can see, I think what you're reacting to is the contrast between the tile surround and the floor, not the tile surround and the paint, which looks fine to me. The floor is definitely a warmer tone than the mosaic marble tile.

Since this is self-stick tile--presumably easy to remove--and I'm assuming you don't want to go to the expense of changing out your flooring, I might try to find a different marble tile that has more gold/caramel accents in it.

If that's carpet on the floor, you need a fireproof hearth in front of the firebox--brick, tile, whatever. The carpet should not be right up against the surround. It's a fire hazard. Even if you remove the carpet and lay down hardwood, you still need a hearth.

Not a Pro.

Try taking your area rug out of the room for now and see that quiets the room.

I agree the fireplace and bookshelves and mantle colors work fine together. The carpet is what needs to be a gray or white. What will the new flooring look like? Maybe you need to be sure it still works now that you have this new element. As far as warming the place up, well you chose cool colors for the newest elements...so not sure what to suggest. The area rug is cool colors, and covers up the clashing carpet so not sure removing it will help your frustration.