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Review those packets you attached once more. They appear to me to contain most of the answers for the blanks.
For this question, we need to understand that heat is always transfered from hot to cold. This is the zeroth law of thermodynamics. The thermal energy of the outside air is conducted through the material of the tank and into the water. This transfer of heat from the air creates a temperature gradient (Are you familier with fluid dynamics/mechanics and the ideas of boundary layers?) and this temperature gradient extends out into the fluid. See figure below|dw:1326824307960:dw|Note the curved lines. These temperature gradients create convection currents which enhance the heat transfer from the air to the tank wall and the tank wall to the water. This is known of free convection because we are not manually moving the air. Lastly, because there exits a temperature difference between the fluids and the wall, radiation will exist.
As we can see, a temperature gradient is always needed for any type of heat transfer to occur.