To understand the behavior of solubility, it is helpful to look at the chemicals that misbehave, and apply the rules, and look for underlying explanations and common threads. Generally speaking, the solubility of some chemicals is lower at higher temperature.
The problem is, the explanation(s) for this is that entropy is negative for some chemicals, and solvation is difficult, and sometimes- the hydrated phases change (which is more like a chemical reaction, where the resultant chemical precipitates). So, I would like to identify the chemicals which misbehave and identify the explanation(s) or the excuse(s).
Here are a couple of links to other questions on this SE about this phenomenon:
What are some chemicals that dissolve better in cold water than hot water?