[math-fun] Physics question

Suppose there was a closed glass cylinder, with a thin planar membrane separating the cylinder into two chambers. The chambers contain colored water of two different colors, having the same density and no chemical reaction with one another. The water in one chamber is warmer than the water in the other chamber, but we do not know what color water is warmer. The cylinder is put into a zero-gravity environment, allowed to come to rest, and the membrane is removed, allowing the water allowed to mix. Can we tell by the flow patterns of the mixing water which color is warmer and which cooler?