Outdoor stone fire pit has cracked because of heat

I recently Built a fire pit on my patio and built the bottom in fire brick with fire clay added to the mortar. Then built the walls useing local stone that was double walled and capped with flag stone all set with mortar with no fire clay. This weekend was cold and I started a fire of good size. once that happened the stones on the inside of the fire pit cracked and the flagstone caps did the same. I am now going to redo the pit with fire brick for the inside wall then stone on the outside all with fire clay added to the mortar. My question is there any type of stone that would make a good cap since the flagstone can not seem to hold up to the heat? Any suggestions would be great.