Imagine a cake in your convection oven. The cake is being heated by the circulating air (convection). It is also being heated by being in physical contact with the hot grills of the oven (conduction).
I'm not sure about this... isn't convection actually fliud movements due to change of energy?
When gas or liquid heats up, the increased energy causes a lessening of density, so the gas rises. It cools down while rising, becoming more dense again and then sinks.
I guess energy is being transfered by the movements of the fluid, but the way you phrased it seemed backwards to me.