We use the cosmo-OWLS suite of cosmological hydrodynamical simulations, which includes different galactic feedback models, to predict the cross-correlation signal between weak gravitational lensing and the thermal Sunyaev-Zeldovich (tSZ) $y$-parameter. The predictions are compared to the recent detection reported by van Waerbeke and collaborators. The simulations reproduce the weak lensing-tSZ cross-correlation, $xi_{ykappa}(theta)$, well. The uncertainty arising from different possible feedback models appears to be important on small scales only ($theta lesssim 10$ arcmin), while the amplitude of the correlation on all scales is sensitive to cosmological parameters that control the growth rate of structure (such as $sigma_8$, $Omega_m$ and $Omega_b$). This study confirms our previous claim (in Ma et al.) that a significant proportion of the signal originates from the diffuse gas component in low-mass ($M_{rm{halo}} lesssim 10^{14} M_{odot}$) clusters as well as from the region beyond the virial radius. We estimate that approximately 20$%$ of the detected signal comes from low-mass clusters, which corresponds to about 30$%$ of the baryon density of the Universe. The simulations also suggest that more than half of the baryons in the Universe are in the form of diffuse gas outside halos ($gtrsim 5$ times the virial radius) which is not hot or dense enough to produce a significant tSZ signal or be observed by X-ray experiments. Finally, we show that future high-resolution tSZ-lensing cross-correlation observations will serve as a powerful tool for discriminating between different galactic feedback models.
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