Low-frequency, high-amplitude pH-oscillations observed experimentally in the H2O2-HSO3--S2O32- flow reaction system at 21.0 degrees C undergo period-doubling cascades to chemical chaos upon decreasing the temperature to 19.0 degrees C in small steps. Period-4 oscillations are observed at 20.0 degrees C and can be calculated on the basis of a simple model. A reverse transition from chaos to high-frequency limit cycle oscillations is also observable in the reaction system upon decreasing further the temperature step by step to 15.0 degrees C. Period-2 oscillations are measured at 18.0 degrees C. Such a temperature-change-induced transition between periodic and chaotic oscillatory states can be understood by taking into account the different effects of temperature on the rates of composite reactions in the oscillatory system. Small differences in the activation energies of the composite reactions are responsible for the observed transitions. Temperature-change-induced period doubling is suggested as a simple tool for determining whether an experimentally observed random behavior in chemical systems is of deterministic origin or due to experimental noise.