That old sweater protected you from the cold, but it'll protect your tabletop from heat when you turn it into a felted trivet. Wash the sweater (it must be at least 80 percent wool) with detergent on your washing machine's hottest setting. Dry it at the highest temperature as well. (To get the properly thick felted texture -- matted and no longer unraveling -- you may need to repeat the process.) Then cut the felt to any size, and shape it as you like with a rotary cutter or craft scissors.
Martha Stewart Living, March 2013