The H2O2-S2O32--H+-Cu2+ dynamical system exhibits sustained oscillations under flow conditions but reveals only a single initial peak of the indicator electrode potential and pH variation under batch isothermal conditions. Thus, in the latter case, there is no possibility of the coupling of the oscillations and diffusion which could lead to formation of sustained spatiotemporal patterns in this process. However, in the inhomogeneous temperature field, due to dependence of the local reaction kinetics on temperature, spatial inhomogeneities of pH distribution can develop which, in the presence of an appropriate indicator, thymol blue, manifest themselves as the color front traveling along the quasi-one-dimensional reactor. In this work, we describe the experimental conditions under which the above-mentioned phenomena can be observed and present their numerical model based on thermokinetic coupling and spatial coordinate introduced to earlier isothermal homogeneous kinetic mechanism.