Exciton radiative recombination lifetime in a thin quantum box in the intermediate spatial dimension between the two-dimension and the zero-dimension is investigated by a theoretical analysis which rigorously treats the electron-hole Coulomb interaction. The higher exciton states as well as the ground exciton state are explicitly taken into account to estimate the temperature dependence of exciton recombination lifetime. We clarify how the temperature dependence of the recombination lifetime varies with a change in the quantum confinement dimension which can be controlled by the lateral width of a thin quantum box. We also discuss the effect of the exciton localization due to structural imperfection on the radiative recombination lifetime.