Surface warming since 1950 in the off‐equatorial south Indian Ocean (IO) occurs without a consistent surface heat flux trend, and is accompanied by a shoaling thermocline. The associated dynamics have not been fully explored. Using 20th century climate model experiments, we test if the shoaling thermocline is attributable to a transmission from the Pacific, where a similar shoaling occurs, and whether it is climate change‐induced. A 22‐model average produces no such signal. An average of a subset of models that better simulate El Niño‐Southern Oscillation (ENSO) and its transmission produces the right direction of the IO thermocline trends. The shoaling in this subset average, taken as anthropogenically induced, is far weaker than the observed, suggesting a significant multidecadal variability component in the observed changes. The Pacific contribution increases with a stronger model ENSO amplitude and broader meridional structure, highlighting the importance of realistic ENSO simulations in modelling long‐term change in the IO.