Changes in ocean circulation associated with internal climate variability have a major influence on upper ocean temperatures, particularly in regions such as the North Atlantic, which are relatively well-observed and therefore over-represented in the observational record. As a result, global estimates of upper ocean heat content can give misleading estimates of the roles of natural and anthropogenic factors in causing oceanic warming. We present a method to quantify ocean warming that filters out the natural internal variability from both observations and climate simulations and better isolates externally forced air-sea heat flux changes. We obtain a much clearer picture of the drivers of oceanic temperature changes, being able to detect the effects of both anthropogenic and volcanic influences simultaneously in the observed record. Our results show that climate models are capable of capturing in remarkable detail the externally forced component of ocean temperature evolution over the last five decades.