The Indo-Pacific warm pool (IPWP), which affects the global climate system through supporting tropical convection, has been reported to expand significantly under greenhouse warming. Although early research revealed that the sea surface temperature (SST) threshold for deep convection (σSST_conv) increases with global warming, many latest works on the IPWP expansion were still conducted based on the traditional IPWP definition (e.g., static SST=28°C threshold, and is referred to as the oceanic warm pool, OWPSST=28). Here, using the latest observations and climate model simulations, by considering the long-term variability σSST_conv, we define the deep convection favoring pool (DCFP) over the Indo-Pacific Ocean, which reflects the region where with local SST favors occurrence of deep convections, under past and future climate change. Result based on observations from 1979–2020 shows that because of the increase of σSST_conv under climate change, the DCFP expands at a rate 2.6 times slower than the OWPSST=28, and is more consistent with the change in deep convection area. In the future climate (2015–2100), CMIP6 models projected that the σSST_conv¬ will further increase, with a larger trend under higher emission scenarios. As a result, the increasing trend of the DCFP area is 12–27 times smaller than that of OWPSST=28 under the SSP1-2.6, SSP2-4.5 and SSP5-8.5 scenarios. While the OWPSST=28 expands to the eastern Pacific, the DCFP will remain within the Indian Ocean and western Pacific Ocean regardless of the emission levels. The consistency between the area changes of the DCFP and deep convection area implies that the IPWP expansion estimated based on the fixed σSST_conv may not reflect the direct impacts of Indo-Pacific warming on the climate system under greenhouse warming. This study emphasizes the necessity of considering the response of the relationship between deep convection and SST to climate change when studying the long-term variability of the IPWP, and claims that the DCFP serves as a more reasonable reference of IPWP expansion.