I agree that the darker color of the dye can raise water temps, but I think by limiting the sun to the deeper water it might be cooler at depth and create a larger difference between surface water and the bottom.
That's kind of what I was thinking might have been the case, AP, but I was also thinking that if the upper water was getting more distinctly heated, would that not translate to more transferred heat into the next layer and so on? I realize that thermoclines will play a role in it, but it just seems that if your top water is warm, at least the next layer is going to gain some of that heat, too.