Janus monolayers have emerged as a pivotal platform for next-generation nanoelectronics due to their intrinsic broken mirror symmetry and strong sensitive response to external fields. In this work, we systematically investigate the strain-gradient-induced evolution of electronic structures and thermal transport properties in monolayer Janus STe₂ using first-principles calculations. By constructing three distinct corrugated architectures—Armchair ripple, Zigzag ripple, and Wrinkles—we introduce non-uniform strain fields to break the inherent lattice symmetry.Our findings reveal a universal semiconductor-to-metal transition (SMT) driven by the narrowing of the bandgap as the wrinkle amplitude increases. Notably, the Wrinkle configuration exhibits the highest modulation efficiency, triggering the SMT at a critical amplitude of 0.6 Å. Detailed analysis of the projected density of states (PDOS) and electronic localization function (ELF) elucidates that this transition is rooted in the orbital-selective response of Te-5p states. The strain gradient induces a significant redistribution of charge from compressed regions to tensile zones, enhancing the covalent character of S-Te bonds and establishing long-range delocalization pathways via reconstructed "S-Te-Te" coordination.Regarding thermal transport, the electronic thermal conductivity κ_e of Jκ_e undergoes a dramatic leap of nearly two orders of magnitude under strain gradients, reaching values comparable to bulk copper (425.36 W·m^-1·K^-1). We demonstrate that the transport behavior is highly configuration-dependent: the Armchair ripple creates a high-contrast directional heat channel with a significant κ_x/κ_y anisotropy ratio, while the Zigzag ripple provides superior isotropic dissipation pathways in the high-deformation regime due to intensified interlayer orbital hybridization. These results not only clarify the microscopic bonding-to-transport consistency in Janus systems but also provide a robust theoretical framework for designing flexible, high-performance thermoelectric and heat-management devices based on strain-gradient engineering.