To get burn marks out of a sink take some baking soda and sprinkle the baking soda onto the burn mark in the sink.
Then pour or spray some vinegar onto the baking soda and burn mark and allow it to sit for 10 to 20 minutes.
Then take a scrub brush or sponge and scrub the burn mark off the sink.
The vinegar and baking soda should easily remove the burn mark but if the burn mark is being stubborn to remove you might need to try adding some more baking soda and vinegar again and allow it to sit another 20 minutes or so and then try scrubbing it again.
I've had good luck using the baking soda and vinegar to remove burn marks from my sinks as well as other stains.