Methods for the solventless transesterification of a polyol comprise reacting polyol with fatty acid alkyl ester in the presence of a basic catalyst to produce polyol fatty acid polyester product and lower alkyl alcohol by-product, wherein a majority of the polyol is fully esterified. The reaction is conducted in a reactor at a temperature in the range of from about 60.degree. to about 180.degree. C. and at atmospheric or superatmospheric pressure. An inert gas is sparged through the reactor with sufficient mass transfer surface area contact between the inert gas and reactor liquid to transfer the lower alkyl alcohol by-product from a liquid mixture of reactant and product to the inert gas and promote full esterification of a majority of the polyol without the use of vacuum pressure.