In a zero carbon future but with increasing energy requirements would Earths oceans continue heating? We’ve completely obliterated our reliance on carbon based fuels. All our energy comes from renewal resources or even fusion. Our energy requirements continue to rise. Taking this to a deliberately ludicrous degree, whereby we’re capturing the sun’s energy, planet wide, via solar panels, we would essentially be diverting large amounts of sunlight that might otherwise have reflected our radiated back into space into our energy networks. Whatever that energy is used for our will ultimately be transformed Into heat. Some of that heat will be emitted into space via radiation, but I can’t help wondering if much of it will just stick around and continue to heat our atmosphere and oceans. Could our energy consumption increase indefinitely without affecting the ability of Earth to support our current ecosystem; or will be ultimately have to limit our energy use?

Edit for disambiguation purposes:
I'm not sure my original question at posed has been understood. Ignoring existing greenhouse gas emissions, in fact ignoring any issue with GHG at all, as civilization advances and our energy requirements continue to rise, the energy that we do use to perform work will ultimately be transformed into heat. We'd basically be pumping heat into the atmosphere instead of GHGs. A hotter atmosphere still holds more energy and moisture. Could we end up overproducing heat via fusion? Or is radiation an effective way for the planet to balance this excess?
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.