It doesn't matter how carpet burns happen, by iron or cigarette, all burn repairs are repaired the same way. The burnt carpet is removed and replaced with what is known as a "donor piece". Either a spare piece of carpet or a piece removed from the closet.

Although this is a quick view of how this repair is done, if you are more interested you are welcome to watch while the repair is completed. Possibly you will be as intrigued and satisfied as I am with the successful completion of each repair.