The present invention is based on the finding that stearin fats, obtainable by dry or solvent fractionation of sunflower high-stearic and high-oleic oils, optionally with seeding with tempered stearin crystals, have a high solid fat content at temperatures higher than 30° C., even higher than cocoa butter or other high saturated tropical fats with a similar disaturated triacylglycerol content due to the presence of disaturated triacylgiycerols rich in stearic acid, and improved melting point due to the presence of arachidic and behenic acids in these disaturated triacylgiycerols, being at the same time healthier that actual fats made from palm, palm kernel and coconut oils, or hydrogenated and trasesterified vegetable oils.