In this work, we studied the kinetics of the oxidation of iodide ion by persulfate ion in the critical water/bis(2-ethylhexyl) sodium sulfosuccinate (AOT)/n-decane microemulsions with the molar ratios of water to AOT being 35.0 and 40.8 via the microcalorimetry at various temperatures. It was found that the Arrhenius equation was valid for correlating experimental measurements in the noncritical region, but the slowing down effect existed significantly in the near critical region. We determined the values of the critical slowing down exponent and found it to be 0.187 +/- 0.023 and 0.193 +/- 0.032, respectively, which agreed well with the theoretical value of 0.207 predicted by the Griffiths-Wheeler rule for the singularity of the dimer/monomer droplet equilibrium in the critical AOT/water/n-decane microemulsions.