How do you determine if a salt has a change in solubility as temperature increases?
How else but by experiment...........?
Of course, you have to find a suitable method of analysis, and if you have to ensure that the solution is saturated at a particular temperature (and these caveats may be non-trivial to establish).
The signals emitted by a suitable radioactive isotope are sometimes utilized to determine solubility. Given a salt, with strong interparticle forces of attraction, we would ASSUME that as temperature increases, solubility increases. This is not always the case.