The propagation of detonations in a non-uniform mixture exhibits notable distinctions from that in a uniform mixture. This study first delves into the analytical analysis of the one-dimensional shock transmission problem and the two-dimensional shock propagation in a mixture with temperature non-uniformity. Additionally, the research extends to the numerical simulation of the propagation of shocks and detonations, building upon the insights garnered from the analytical analysis. The numerical results indicate that introducing a temperature interface in a non-uniform gas creates a discrete flow field and wavefront, resulting in oblique shocks that connect hot and cold layers. A competitive mechanism between the transverse waves and non-uniformity is responsible for the detonation propagation. The temperature amplitude tends to inhibit the propagation of transverse waves. In contrast, the wavelengths primarily affect the spacing and strength of these transverse waves, especially during the early stages of propagation. In a Zel’Dovich–von Neumann–Döring detonation, the non-uniformities distort the detonation front, creating transverse wave spacings comparable to the wavelength and reducing the front velocity. However, the detonation can recover its Chapman–Jouguet velocity and approach a steady states as intrinsic instabilities come into play. In the steady state, the cell sizes are found to be determined by the temperature amplitude. When the temperature amplitude is sufficiently high, the detonation cells effectively disappear.