In a zero carbon future but with increasing energy requirements would Earths oceans continue heating?
Short answer: Yes, the ocean would continue heating for a while if we cut off all greenhouse emissions. Simply because CO2 has a long life span in the atmosphere and its effects will continue to be active for a long time, longer than human life spans.

Also, it may be that thresholds have already been passed that lead to positive feedbacks, like glacier retreat or desertification that amplify the forcing effects of greenhouse gases. Deforestation and wild fires are another such positive feedback, they release a lot of CO2 for immediate warming effect and expose a surface ready to be eroded and not available as a carbon sink any more.