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. 10-4 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.