Our mum makes a lot of jelly and jam, and she always sterilizes her jars in the oven. She'll take a piece of newspaper, soak it in water, use it to line a cookie sheet, and then set her jars on it in the oven. Then she keeps them in there, with the oven turned on, until she needs to use them. She sterilizes her lids by boiling them in a pot on the stove, and she keeps them simmering until she needs them, too.
Nobody has ever gotten sick from any jam or jelly that she made.