Wood is always susceptible to burns. Tables and countertops made of wood are even more so. Candles, cigarettes and hotplates can cause burn stains on the wood. Heavily burnt woods may not be repaired but light surface burns can be removed completely or cleaned with the right tools. When trying to remove the stain, work slowly so you do not damage the finish of the wood. This will create more work than necessary.
Rub lemon juice using a soft cloth onto burn stains from hotplates. Rub slowly to remove the stain.
Rub a tough stain with a 0000 grade steel wool dipped in lemon oil, moving along the grain. Check the stain at each pass to make sure you are only removing as much as necessary. Lemon oil is available from hardware stores and some grocery stores.
Mix together linseed oil and rottenstone, available from your hardware store, until it makes a paste. Rub the paste into the stain, going with the grain, to remove it.
Use pure lemon oil to remove the stain. Impure lemon oil has petroleum in it which can make your furniture a fire hazard. Look at the label of the bottle. If it is flammable, the lemon oil is not pure.