Cleaning out coffee pots and thermoses
We brew beer at home, so we have a product that does a really good job of this, called PBW (Powdered Brewery Wash). Our stainless steel coffee thermoses come out like new. The product description from a site that offers it reads:


  PBW (Powdered Brewery Wash) is a patented alkali cleaner originally developed for Coors, now widely used in commercial breweries across North America. Use 1 to 2 ounces per gallon for cleaning kettles, 3/4 ounce per gallon for fermenters, kegs, tanks, and other equipment. Soak equipment overnight in PBW solution; rinse the following morning - no scrubbing required! Will not damage rubber gaskets, soft metals, or your skin. PBW can effectively clean items that can't be reached with a brush or sponge, and is strong enough to remove thick, difficult, caked-on organic soils.


That said, we already have this product. I've been doing some research and it sounds like Oxiclean actually works about as well and you may already have some at home - and if not, you can likely find it more easily.