The tropical Pacific response to radiative forcing remains uncertain as projected future changes to the Walker circulation and SST patterns vary substantially among climate models. Here, we study what sets the magnitude and timescales of the response and why they differ across models. Specifically, we compare the fast and slow responses of the tropical Pacific to abrupt CO₂ increases (2, 4, 8, 16 × CO₂) in two configurations of the same model family (CESM) that differ in horizontal resolution and mean biases. We find that the model with a higher resolution shows a transient ocean thermostat-like response to CO₂-forcing, with a stronger Walker cell and lack of warming in the eastern Pacific trade wind belts. This fast response lasts for about 50 years and is followed by a slight Walker cell weakening and equatorial warming. The second model, with a coarser resolution, shows a weak and short-lasting ocean thermostat response, followed by pronounced Walker cell weakening and eastern equatorial Pacific warming, similar to the long-term pattern noted in previous studies. These fast and slow responses also manifest in experiments where CO₂ is gradually increased. We relate the magnitude of the fast ocean-thermostat response to the structure of the equatorial thermocline, setting the strength of the Bjerknes feedback. The magnitude and timing of the delayed eastern equatorial Pacific warming are related to the competition of positive feedbacks amplifying the ocean thermostat against the effect of ocean subsurface warming eroding the thermostat. The latter effect is further amplified by the slowdown of oceanic subtropical cells and enhanced extra-tropical warming. Different balances between these effects could explain the large spread in the model future projections for the tropical Pacific.