The activation energy is zero. The rate constant of the reaction

According to Arrhenius Equation,

$\mathrm{K}={\mathrm{Ae}}^{-{\mathrm{E}}_{\mathrm{a}}/\mathrm{RT}}$

If ${\mathrm{E}}_{\mathrm{a}}=0 \mathrm{and} \mathrm{then} \mathrm{K}=\mathrm{A}$

In these conditions, the rate constant of the reaction is nearly independent of temperature.