If it's level and if the edge of the tile is straight, I would make a threshold that butts into the tile, rabbetted out so it just lips over the top of the wood, sloped down to a 1/8" reveal. The rabbet would give the wood some expansion space. It should be relatively easy to find a piece of suitable 3/4" thick Oak and the whole thing could be made on a table saw. Make it, finish it, install plywood layers in the gap to build it up, then either glue or pin it down.
It would be somewhat like this picture http://www.greenflooringsupply.com/wordpress/wp-content/uploads/Baby_threshold.jpg if you were to cut off the slope on the right side and butt the piece to the edge of your tile. If the edge of the tile's not perfectly straight, you could still do this, but place the threshold a full to half grout joint width from the tile, then grout the gap.
It would be somewhat like this picture http://www.greenflooringsupply.com/wordpress/wp-content/uploads/Baby_threshold.jpg if you were to cut off the slope on the right side and butt the piece to the edge of your tile. If the edge of the tile's not perfectly straight, you could still do this, but place the threshold a full to half grout joint width from the tile, then grout the gap.