The road to solvation 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:

Why do some solid chemicals dissolve better in colder water? and Why does sodium sulfate have an unusual solubility-temperature curve?.

What are some chemicals that dissolve better in cold water than hot water?
Calcium acetate, calcium hydroxide, calcium phosphate, cerium(III) selenate, cerium(III) sulfate, and lithium sulfate are more soluble in cold water than hot water. 

Also, calcium selenate seems to have it's highest solubility at around 10 °C; and sodium sulfate has it's highest solublity at around 32 °C. These two chemicals have phase changes.

Gases (like oxygen) are also generally more soluble in colder water. The primary explanation is that colder temperatures and higher pressure results in gas becoming a liquid.