We have investigated the temperature-dependent photoluminescence (PL) characteristics of stacked self-assembled InAs/GaAs quantum dot structures grown by molecular beam epitaxy (MBE). A step-like behavior of the peak energies of excitonic bands as a function of temperature is observed in two temperature ranges of 60-90 K and 120-150 K, while the envelope of the change of peak energies basically follows the Varshini law with InAs parameters up to 150 K. The thermal activation energy of the electron-hole emission through a GaAs barrier in the quantum dots was measured to be 76 meV. We observed an unusual increase of integrated photoluminescence intensity with temperature in the step regions, suggesting that the excitonic recombination in stacked quantum dots occurs in a condition where higher oscillator strength occurred with a certain lattice temperature.