The melting point of gold is 1947.52 deg. F. There is little chance your fireplace ever gets anywhere near that hot.
Aluminum melts at 1200 deg. F. Toss a Pepsi can in the fire sometime and watch how long it takes to start to even droop. Even then it will not melt completely down into a solid blob.
If you would have sifted the ashes through a screen after the fire burned out. You probably would have found your ring completely unharmed.
If you know where you buried the ashes... It's probably still there.