Sugar can indeed cure a burnt tongue.
If you've burnt your tongue on a hot drink or hot food then putting some sugar on your tongue and pressing the sugar into the tongue a little can help with the burning pain of the burnt tongue.
Also drinking some milk or gargling some milk can help with a burnt tongue as well.
But if your tongue is just burning and you haven't burnt your tongue with any food, hot drink etc then you may have burning mouth syndrome.
If your tongue is suddenly feeling like it's burned and constantly feels like your tongue is burned you may have burning mouth syndrome.
Burning mouth syndrome can make your tongue and sometimes your mouth feel like it's burning as well as a bitter or metallic taste; Loss of taste; Tingling, stinging as well as numbness in your mouth or tongue.
Burning mouth syndrome will usually go away within a few days or so but if not see your doctor about it.
Your doctor can prescribe you medications to help ease the pain of the burning mouth syndrome.
You should also increase your intake of water and even eating spicy foods can help get rid of the burning tongue or burning mouth.
Yes the spicy foods will burn your tongue and mouth but it will help to work against the burning mouth syndrome and help stop the burning of the tongue from it as well.