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The limited historical observational sampling of the ocean gives rise to uncertainty in time series of global ocean temperature anomalies calculated from those observations. Without knowledge of the true global state of the oceans, it is difficult to characterize the errors caused by these sampling issues. One way to quantify them is to use climate model data. Pseudo observational time series can be constructed from the model data using knowledge of where observations occurred. Comparison of these with time series constructed from the full model fields yields information about how observational sampling impacts time series of the temperature change in the modelled world. This can then be related back to the time series generated from the real observations. In this study, climate model data were used to investigate sampling errors in 0-700 m global average ocean temperature anomaly time series calculated using a straightforward gridding approach. The sampling had two impacts. First, sampling causes issues with constructing a climatology that is representative of the long-term average state of the ocean. Climatology errors were shown to have the potential to cause systematically changing errors in anomaly time series. Second, some regions of the ocean were poorly observed prior to improvements brought about by the Argo project. This was found to cause spurious variability, both year to year and over multi-year time scales. The latter had similar magnitude to the actual multi-year variability seen in the model data but was smaller than the model's long-term temperature change. The features of these errors depend on the ocean state and therefore varied between climate model runs. More sophisticated methods used to calculate ocean temperature time series are expected to be less impacted by sampling. Nevertheless, sampling errors will still occur and therefore this type of study is recommended even for those techniques.