I hate trying to carve tiny chunks of clay to work with so i put the block of clay in a thick ziplock wrap that with a towel, take it out to the garage and run it over with the old Chevrolet capri a time or two
then I can just break off some and warm it. To warm my clay I use one of those candle warmers. You place a ceramic tile or ceramic bowl on top and it works great. If it gets to hot put lift the bowl by placing it inside another. I also put a bit of oil in the bowl to keep the clay from sticking.