OK, I know what you mean... but I still don't think that's diffusion limited. Diffusion speed is limited by the collisions and random walk of the molecules; you don't have these when the gas is expanding.
As I understand the question you have gas in a closed expandable container and you heat it - so the speed of volume changes depends only on the heat transfer inside of the tank. But perhaps my understanding of the question was skewed by the fact, that I have tried to make sense out of it - so I assumed gas is in the container, as otherwise there will be no final volume...
Now, even if you put the gas into already heated container, it have to be heat up - as it is not stated what is the starting temperature of the gas. Jeez, the longer I try to make something out of it the worse it looks. Time to shut up