Tropical instability Waves (TIWs) dominate intraseasonal variability in the tropical Pacific Ocean, and strongly impact tropical ocean dynamics and marine ecosystems as well as modulating tropical climate variability. However, TIWs' response to future greenhouse warming remains relatively unexplored because most current climate models cannot resolve TIWs well. Here we use a suite of TIW-resolving climate model simulations to reveal that there is a consistent decrease in TIW-driven temperature variability under CO2 increases, mainly due to the weakening of the meridional sea surface temperature gradient. Two distinct mechanisms affect TIW changes: north of the equator, there is an intensification of the Rossby mode, possibly as a result of increasing instability of the major equatorial current. This creates a stronger ocean momentum flux feedback on zonal flow. Along the equator, the combination of increased current shear and decreased temperature gradient creates a net decrease in the Yanai mode and a correspondingly weaker equatorial ocean heat flux feedback on mean temperature. On seasonal timescales, the result in all models examined is a weakening of variability in both cold tongue temperature and zonal flow. Our results point to improvement in TIW simulations as a key pathway for reducing uncertainty in tropical Pacific climate projections.