Cleaning and Stain Removal - Heat Stain On Oak Dining Room Table

My wife baked cookies for Christmas and doubled the table cloth as a heat shield after taking the cookies off of the cookie sheet. Afterwards there was heat marks the shape of the cookies on the table. We didn't try anything to take the stains off yet. I think the table is stain and Polyurthane finish on it. Any suggestions what to use.
Thanks Joe

Cover stains with mayonnaise and sprinkle on some cigarette or wood ashes. Rub back and forth with soft cloth in direction of wood grain. Repeat applications may be necessary. Or, rub stains with toothpaste and baking soda. Take damp corner of cloth and dip into baking soda and then toothpaste. If stains remain heat with blow dryer and rub with soft cloth in direction of wood grain. Lastly, you can try rubbing with #0000 steel wool in direction of grain. If stains remain the table will likely have to be refinished.

Thankyou for your invaluable info. I used the toothpaste and baking soda mix, and it removed the heat stains from our dining room table, that was just refinished a year ago. Worked brilliantly. Again, many thanks!!!!