<p>Moiré superlattices created by twistronics generate flat bands for enabling localization in topological and quantum system. Most prior realizations rely on nonlinear interactions among electrons, photons, or other particles to achieve moiré-driven localization. However, the intrinsically diffusive and momentum-free nature of thermal conduction poses a fundamental challenge to implementing moiré physics in a linear regime. In contrast to exploiting nonlinearity, we demonstrate moiré-induced thermal localization in a linearly coupled bilayer conductive system with spatially engineered diffusivity. By tuning the twist angles, we create both commensurate and incommensurate moiré patterns, each governed by two distinct modulated wavevectors controlling global periodicity and local unit-cell structure. Aperiodic thermal localization emerges in incommensurate quasicrystals with the transition threshold linked to the emergent lattice constant. Our results establish a paradigm for implementing moiré physics in a static, linear, and momentum-free diffusive system, offering a route to geometrically programmable non-equilibrium control in heat and mass transport.</p>