How are solubility and temperature generally related in a system consisting of a solid solute and a liquid solvent?

Solubility and temperatures are directly related. The higher the temperature of the solvent, the higher the solubility of the solute in the solvent.

Dissolving a solute in a solvent is an endothermic process hence providing heat favors the process. Higher temperatures cause the molecules of the solvent to have high kinetic energy hence bombard each other and with that of the solute with high frequency. This then ensures fast diffusion of the solute particles in the solvent.