Yes, Bluestone absorbs heat quite well.
It is a flat, fairly soft, puros stone. The only place in the world that has it are that part of NY and PA. Bluestone mining and Logging are big industries up there, especially as the farming has receded. Mostly Hard Maple, Ash, Black Cherry, and Red Oak. There are also some Birch and Beech, but I never see any White Oak, Chestnut Oak, Tulip or Hickory up there, all of which are fairly common down here. Logging is generally only trees over 14" diameter, there is no clear cutting.
It is ideal for walkways, steps and patios because you will not slip when it is wet. It is also very commonly used for windowsills and fireplace mantles.
In my old (small) cabin I have two pieces of it against the wall where the woodstove is. I tell folks I have "real sheetrock"!