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Coupled Model Intercomparison Project (CMIP5) models project an inhomogeneous anthropogenic surface warming of the Indian Ocean by the end of the 21st century, with strongest warming in the Arabian Sea and Western equatorial Indian Ocean. Previous studies have warned that this "Indian Ocean Dipole (IOD)-like" warming pattern could yield more Arabian Sea cyclones, more extreme IOD events and decrease monsoonal rains. Here we show that CMIP5 models also produce an "IOD-like" pattern over the 1871-2016 period, in broad agreement with observations. Single-models ensemble simulations however indicate a strong aliasing of the warming pattern "signal" by the internal climate variability "noise" over that period. While the average Indian Ocean warming emerges around 1950 in CMIP5 and observations, regional contrasts are more difficult to detect. The only detectable signal by 2016 in CMIP5 is a stronger Arabian Sea than Bay of Bengal warming in > 80% of the models, which is not detected in HadSST3 observations. Conversely, observations already detect a stronger Northern than Southern Indian ocean warming, while this signal only emerges by similar to 2060 in > 80% of the models. Subsampling observations to only retain the most accurate values however indicate that this observed signal most likely results from sampling issues in the Southern hemisphere. In light of this large aliasing by internal climate variability and observational uncertainties, the broad agreement between CMIP5 and observations over 1871-2016 may be largely coincidental. Overall, these results call for extreme caution when interpreting spatial patterns of anthropogenic surface warming.