For some reason I’m not into finding the exact info, but it is available; I’ve seen it calculated. I think the heating potential of the oceans is something like 400 times that of the atmosphere.
I would accept that. My calculation was about the simplest one could make. The atmosphere probably holds more heat than I assumed because the heat capacity does not decrease with decreasing pressure as much as my simplified calculation assumes.
My exercise was just to show that even the simplest model of the heat capacity of oceans and atmosphere would rule out ignoring the oceans.