Body Warmer is an elixir mentioned in the fourth book, Neverseen, by Dex in response to Coiffe's bizarre appearance.
While the others there had mixed reactions to Coiffe, Dex's form of reply was a bit different than all of these, as he inferred what Timkin had used for his looks.
His guess was that a few drops of Body Warmer and a lot of Curly-dew and Macho-Macho was used. It is unknown exactly what it does.
All of these elixirs are familiar to Dex and are also most likely sold at Slurps and Burps.