One might attempt the problem in terms of total heat content, but 'average temperature' does not pass muster.
If you know the air temperature and the specific heat of the air then you get the internal energy of the air.
For the water it works the same way.
Actually, no. You have the internal energy let's say at the cubic liter where the temperature was noted. Or cubic meter, or something. Take your pick. But both the air and the water are moving around and are stratified layers.
The average of two points each measuring 20C is 20C, the average of one point 0C and another at 40C is 20C. But those describe vastly different environments.
I think you need to know the not just the 'internal energy' for a non linear system, not in equilibrium, but the rate of change of that parameter. Reason is, something that shows 1C higher T and higher heat content, but have a greater rate of energy outflow.
Well, we can discuss this quite a bit, but it would seem that you do get my point.