The present invention relates to a process for preparing a terephthalic diester by reacting terephthalic acid with at least one alcohol, wherein terephthalic acid is suspended in the alcohol in a dispersing tank, the preliminary suspension is passed from the dispersing tank into a reactor and converted in the presence of an esterification catalyst, a reaction suspension is drawn off from a region between the upper region and the lower region of the reactor, a first stream of the reaction suspension is recycled into the upper region of the reactor and a second stream of the reaction suspension is introduced into the lower region of the reactor, and the reaction suspension is thus mixed, wherein the stream drawn off and/or the first stream is passed through a heat exchanger outside the reactor and heated; and water of reaction is distilled off together with the vapor as alcohol-water azeotrope, the vapor is at least partly condensed, the condensate is separated into an aqueous phase and an organic phase and the organic phase is at least partly recycled into the reaction system.