The bonding of silicon-on-insulator (SOI) to lithium niobate-on-insulator (LNOI) is becoming important for a new category of linear and nonlinear micro-photonic optical devices. In studying the bonding of SOI to LNOI through benzocyclobutene (BCB), a popular interlayer bonding dielectric used in hybrid silicon photonic devices, we use thermal stress calculations to suggest that BCB thickness does not affect thermal stress in this type of structure, and instead, thermal stress can be mitigated satisfactorily by matching the handles of the SOI and LNOI. We bond LNOI with a silicon handle to a silicon chip, remove the handle on the LNOI side, and thermally cycle the bonded stack repeatedly from room temperature up to 300°C and back down without incurring thermal stress cracks, which do appear when using LNOI with a lithium niobate handle, regardless of the BCB thickness. We show that this process can be used to create many hybrid silicon-lithium niobate waveguiding structures on a single patterned SOI chip bonded to a large-area (16 mm × 4.2 mm) lithium niobate film.