Numerical experiments on Typhoon Trami (2018) using a regional 1-km-mesh three-dimensional atmosphere–ocean coupled model in current and pseudo-global warming (PGW) climates were conducted to investigate future changes of a slow-moving intense typhoon under the warming climate. Over the warmer sea in the PGW climate, the maximum near-surface wind speed rapidly increased around the large eye of the simulated Trami. The stronger winds in the PGW simulation versus the current simulation caused a 1.5-fold larger decrease of sea surface temperature (SST) in the storm core-region. In the PGW climate, near-surface air temperature increased by 3.1°C. A large SST decrease due to ocean upwelling caused downward heat fluxes from the atmosphere to the ocean. The magnitude of the SST decrease depended strongly on initial ocean conditions. Consideration of the SST decrease induced by an intense typhoon, and a slow-moving storm in particular, indicated that such a typhoon would not always become more intense under the warmer climate conditions. An atmosphere–ocean coupled model should facilitate making more reliable projections of typhoon intensities in a warming climate.