The chap who figured out the diffusion Laws was named Fick, never heard of a Fisk.
As I said before, I can imagine that there are some solutions which may have a significant RI temp. dependence, but I can´t imagine that anybody has conditions which would require an active temp. control of the CELL.
I use an RI with light scattering. In this case, the absolute value of dn/dc is quite important. And, there are very few examples where the value of dn/dc varies enough with temperature to cause problems. Here, "very few" means I don't know of any, but recognize it is a big world.
That said, I haven't seen an RI for batch mode or GPC use that does not have temperature control. To split hairs, the oven surrounding the cell is kept at constant temperature and that eliminates gradients. But, this is the sort of esoteric distinction that usually confuses more than it enlightens (unless you are designing the thing). I don't know of any better way to keep the cell temperature uniform.
Here's a more practical way of looking at things. If you don't have much drift in your RI, the temperature control is "good." If you have a temperature control problem, you will see a lot of drift. Unfortunately, there are lots of reasons for drift. Temperature control is usually at the bottom of the list.