We report the temperature effect on the propagation of excitable traveling waves in a quasi-two-dimensional Belousov-Zhabotinsky reaction-diffusion system. The onset of excitable waves as a function of the sulfuric acid concentration and temperature is identified, on which the sulfuric acid concentration exhibits an Arrhenius dependence on temperature. On the basis of this experimental data, the activation energy of the self-catalyzed reaction in the Oregonator model is estimated to be 83-113 kJ/mol, which is further supported by our numerical simulations. The estimation proceeds without analyzing detailed reaction steps but rather through observing the global dynamic behaviors in the BZ reaction. For a supplement, the wave propagation velocities are calculated based on our results and compared with the experimental observations.