Heat marks on quartz can be removed by carefully buffing the surface with a non-abrasive cleaner such as Bar Keepers Friend or a mixture of baking soda and water until the mark disappears. It is important to avoid using any abrasive or acidic cleaners as it may cause damage to the surface of the quartz. For tougher stains, it is recommended to consult with a professional cleaner or the manufacturers instructions for proper cleaning techniques.