Many submarine slope failures in hydrate-bearing sedimentary deposits might be directly triggered, or at least primed, by gas hydrate dissociation. It has been reported that during the past 55 years (1955–2010) the 0–2000 m layer of oceans worldwide has been warmed by 0.09 °C because of global warming. This raises the following scientific concern: if warming of the bottom water of deep oceans continues, it would dissociate natural gas hydrates and could eventually trigger massive slope failures. The present study explored the submarine slope instability of oceanic gas hydrate-bearing deposits subjected to bottom water warming. One-dimensional coupled thermal-hydraulic-mechanical (T-H-M) finite difference analyses were performed to capture the underlying physical processes initiated by bottom water warming, which includes thermal conduction through sediments, thermal dissociation of gas hydrates, excess pore pressure generation, pressure diffusion, and hydrate dissociation against depressurization. The temperature rise at the seafloor due to bottom water warming is found to create an excess pore pressure that is sufficiently large to reduce the stability of a slope in some cases. Parametric study results suggest that a slope becomes more susceptible to failure with increases in thermal diffusivity and hydrate saturation and decreases in pressure diffusivity, gas saturation, and water depth. Bottom water warming can be further explored to gain a better understanding of the past methane hydrate destabilization events on Earth, assuming that more reliable geological data is available.