Here are some tips: https://spotremoval.coit.com/how-to-get-burn-marks-out-of-carpet
Do you have a picture? Is it a big or small burn? Some can be painted over, others need professional cleaning.
Hi Connie, Here's a video that uses a kit to fix it: https://www.youtube.com/watch?v=c_iDFFdjnIU
And here's a how to video using epoxy https://www.youtube.com/watch?v=bsnNbSBnw_0
My husband used to lay carpet, he had his own business and did the repairs like you mentioned a lot. He cut the square out of the carpet and replaced with with an exact match from a place it won't show (like out of the closet of the same room). Then he used a carpet iron and ironed on the carpet tape. You could rent a carpet iron (you just put the tape under the piece and over lap under the sides of the square under the carpet all the way around) and hold the iron on it. The rental could be done for part of a day (it would take a few minutes is all) and you can buy the tape for it at any carpet store. They could also further advise you. This is the best way to repair it.