Quartz countertops are heat and burn resistant, but only to a certain point. Most quartz countertops can theoretically handle up to 400 degrees F. But, by subjecting the countertop to a swift change in temperature, they could crack.
Another scenario is if you have removed a hot pot from the stove top. You cannot set down the pot directly onto the quartz countertop. The resin that was used to form the countertop is not as heat resistant as quartz. If you place a hot pan onto the quartz, the resin will burn or scorch. The result is a mark and damage that cannot be fixed.
Quartz countertops can stain. However, it is still up to you to keep them clean. Spilled drinks, food scraps, and other substances have the chance to stain quartz countertops. You run the risk of forever staining the countertops and ruining their clean look if not promptly clean up any messes.