In reply to iksander:
A hearth under a woodburner or an open fire?
Under a woodburner in a non-structural joint I suspect most commonly available glues would suffice. Gelled cyanoacrylate would probably be the easiest option. Tape the top surface to prevent the fumes causing a white bloom and scrape the join flat when it's cured.
If it's exposed to direct heat then something cement based and dyed to match in a narrow joint is probably the best bet. Again it would be non structural.
You could reinforce the cold/hidden side with some fiber if need be.
jk