I think that if the arctic ice is having trouble growing now, the year after the first blue ocean it will have a heck of a lot more trouble growing. Since it is November and the ocean is still venting heat, I expect the freezing season to be delayed until at least November, depending mostly on how early the ice disappeared. The date the arctic recovers this year will set a lower boundary for the date the arctic sea ice will start growing after a blue ocean event. If it does not show a recovery this year, then I don't expect arctic sea ice will return in my lifetime
To me that means that arctic air temperatures maybe 20c or 30c above average, perhaps more. Because of all the heat of the Northern Hemisphere tries to go to the arctic, but the arctic will be very warm, heat transfer will be less efficient. But the heat must be transferred, so it will go into places that it doesn't usually go.
More of it will go out into space, somehow, but not likely enough to reverse course. That the atmosphere is richer than average in greenhouse gasses does not help.
More of it will go into melting Greenland and any remaining glaciers in the NH. This will likely cause epic floods in vulnerable areas, as melt rates accelerate. In the long term, places dependent on glaciers for water will face water shortages.
More of the heat will go into the oceans, accelerating sea level rise by virtue of thermal expansion, and causing an acceleration of the extinction rate. Vulnerable cities will be partially or completely submerged for weeks or months. Because of the warmer ocean we might see new atmospheric phenomena like cat 6 hurricanes or perhaps temporary eyes, like in Jupiter.
The heat will also manifest on land. While there is snow left on the NH, snow melt will start sooner than ever, amplifying the heat and setting up forests for disease, drought and eventually fire. Forests become CO2 sources instead of sinks. Places dependent on snow melt for water, will face water shortages.
Heat also goes into melting permafrost. CO2 emissions accelerate even more.
The mid and lower NH should experience long spells of extreme heat waves, but also spells of extreme rainfall due to the acceleration of the water cycle. Places will get stuck in unusual or extreme weather patterns for months.
The interface between the SH and NH winds should change significantly.
To be clear, I think this will all happen the same year, over the course of the year.