We present a theoretical analysis of a novel multi-channel light amplification photonic system on chip, where the nonlinear Raman amplification phenomenon in the silicon (Si) wire waveguide is considered. Particularly, a compact and temperature insensitive Mach–Zehnder interferometer filter working as demultiplexer is also exploited, allowing for the whole Si photonic system to be free from thermal interference. The propagation of the multi-channel pump and Stokes lights is described by a rigorous theoretical model that incorporates all relevant linear and nonlinear optical effects, including the intrinsic waveguide optical losses, first- and second-order frequency dispersion, self-phase and cross-phase modulation, phase shift and two-photon absorption, free-carriers dynamics, as well as the inter-pulse Raman interaction. Notably, to prevent excessive drift of the transmission window of the demultiplexer caused by ambient temperature variations and high thermo-optical coefficient of Si, an asymmetric waveguide width is adopted in the upper and lower arms of each Mach–Zehnder interferometer lattice cell. A Chebyshev half-band filter is utilized to achieve a flat pass-band transmission, achieving a temperature sensitivity of $<1.4\mathrm{pm}/\mathrm{K}$ and over 100 K temperature span. This all-Si amplifier shows a thermally robust behavior, which is desired by future Si-on-insulator (SOI) applications.