To remove heat marks off artificial marble, you can try the following solutions:

1. Vinegar and baking soda: Mix equal parts of vinegar and baking soda to make a paste. Apply the paste to the affected area and let it sit for 10 to 15 minutes. Wipe with a clean cloth and repeat as necessary.

2. Toothpaste: Apply non-gel toothpaste to the heat mark and rub gently with a soft cloth. Rinse with water and wipe dry.

3. Car polish: Apply a small amount of car polish to a soft cloth and rub the heat mark gently. Wipe with a clean cloth and rinse with water.

4. Vegetable oil and baking soda: Mix equal parts of vegetable oil and baking soda to make a thick paste. Apply the paste to the heat mark and let it sit for a few minutes. Wipe with a clean cloth and rinse with water.

It is important to note that these solutions may not work for all types of artificial marble, and it is best to test them on a small, inconspicuous area before applying to the entire surface. Avoid using harsh chemicals or abrasive agents that can damage the artificial marble.