We investigate the effect of changing temperature in the ferroin-catalysed Belousov-Zhabotinsky (BZ) reaction dispersed in the water nanodroplets of a water-in-oil aerosol OT (AOT) microemulsion, which undergoes a temperature-induced percolation transition at about 38 degrees C. We observe stationary Turing patterns at temperatures in the range 15-35 degrees C and bulk oscillations at T = 40-55 degrees C. When a temperature gradient DeltaT is applied normal to a thin layer of the BZ-AOT reaction mixture, the range of patterns observed is dramatically expanded. Anti-phase oscillatory Turing patterns, leaping waves, and chaotic waves emerge, depending on the temperature gradient and the average temperature. These new patterns originate from the coupling between a low temperature Turing mode and a high temperature Hopf mode. Simulations with a simple model of the BZ-AOT system give good agreement with our experimental results.