If oxygen pressure is higher at the surface, it diffuses to lower levels independent of temperature differences.
...but NOT independent of convection, right? And temperature differences would promote convection, right? Water reaches it max. density at 4.5 °C, so heating the uppermost layer of (oxygen-rich) water having a temperature of, say, 1 °C would cause it to sink, no?
Regards,
Warming water causes most dissolved gases to be less soluble. This fact may explain the higher carbon dioxide levels in the atmosphere. Physical Chemistry 101