Accumulation of the reactant supplied to a cooled semibatch reactor (SBR) will occur if the mass transfer rate across the interface is insufficient to keep pace with the supply rate. Then, due to a low starting temperature or supercooling, the reaction temperature does not rise fast enough to the desired value. This accumulation may eventually lead to a temperature runaway. We investigated the possibility of such an event for reactions of the type "chemically enhanced mass transfer" or "fast" and found that only low distribution coefficients, i.e. or lower, can lead to accumulation. At higher distribution coefficients, the mass transfer rate across the interface of a well-mixed dispersion is generally sufficient to prevent accumulation. A thermal runaway in the fast regime exerts a moderate effect, because the effective activation energy is halved. Calculations for the "instantaneous" reaction regime, regarded as a special case of fast reactions, show that there is no runaway possible.