The process is simple. Linseed Oil is poured into shallow tin or lead vessels up to 3 or 4 inches high. These vessels are then covered with glass slabs in a way to allow air to circulate but protecting the oil from dust. The oil is left under direct exposure to the Sun for a number of weeks, being stirred several times each day. It becomes pure and thickens rendering it an excellent oil with optimal drying properties and imparting toughness and elasticity to the oil film.
Sun-Thickened Oil is one of the best choices, both on its own or mixed in oil painting mediums, the use in such mediums being a traditional practice for many centuries. Cenino Cennini did indeed recommended it and in his opinion there could be no better oil then Sun-Thickened Oil. Manufacturers of art materials do not produce this oil unfortunately, so your only choice is actually to make it yourself, but since the process is fairly simple, spare a good bottle of raw cold pressed linseed oil and during the Summer try to make some of this oil yourself. Perhaps one day manufacturers will realize what they are missing by not making this oil, so here is an appeal to them. The best substitute for sun-thickened oil is actually Stand-Oil and for all intents and purposes, any recipes mentioning sun-thickened oil may be safely mixed by replacing it with Stand-Oil.