What is temperature? Part 2

I was cornered the other day by someone who'd taken exception to my stating that convection isn't really a method of heat transfer.

And so to an analogy (feel free to groan I know some hate the ones I produce)

I have a box of tennis balls each marked "HEAT"; you also have a similar box. While moving around we bump into each other and some of each of our tennis balls bounce into the other's box. I end up with less and you end up with more.

Another time I see you standing paying no attention so I take out one of my tennis balls and throw it at you; it lands in your box.

Another time you see me and not wanting to be hit by flung tennis balls you and your box take several steps away from me.

Consider: In the first and second scenarios 'heat' was transferred; you gained it, I lost it. In the third no 'heat' was transferred; it was moved, but it was still attached to you. Conduction, radiation, convection. The question is does the word move and the word transfer have identical meanings? I contend that they don't. I accept that another might and that therefore all three methods do regard heat transfer; however it is still the case that in two of the cases the carriers of heat lose it and one where they don't and for me that continues to stand as a misclassification.