@ToolGuy
What is so complicated about it? As the temperature of the water goes up, there is more energy and thus more chaos in it and the molecules of the dye is dispersed more quickly. If you put the dye in the water and then immediately freeze it, the plume will stay pretty much the same for many thousands of years. As long as the water is kept frozen.
Here's a fun fact. For every ten degrees Celsius rise in temperature, the rate of a chemical reaction will approximately double. The increase of the rate of reaction will generate more heat, which will increase the rate of reaction, thus you get a cascading effect. I don't see any complexity there either.