The concentration of dissolved solute in a saturated solution with endothermic dissolution will decrease with increasing temperature and then increase again with decreasing temperature. This phenomenon can be explained by the principles of Le Chatelier's principle and the solubility-temperature relationship.

1. Le Chatelier's Principle:
- Le Chatelier's principle states that when a system at equilibrium is subjected to a stress, it will respond by shifting its equilibrium position to counteract the stress.
- In the case of an endothermic dissolution process, an increase in temperature can be considered as a stress on the system.

2. Solubility-Temperature Relationship:
- In general, the solubility of most solid solutes increases with increasing temperature. This means that more solute can dissolve in a solvent as the temperature rises.
- However, there are some solutes whose solubility decreases with increasing temperature. These solutes exhibit an endothermic dissolution process.

Now, let's analyze the effect of temperature on the concentration of dissolved solute in a saturated solution with endothermic dissolution:

- Increasing Temperature:
When the temperature is increased, the stress on the system causes the equilibrium to shift in the direction that consumes heat. In this case, as the dissolution process is endothermic, the dissolution reaction is favored in the forward direction to absorb the excess heat.

- Decreasing Temperature:
When the temperature is decreased, the stress on the system causes the equilibrium to shift in the direction that releases heat. In this case, as the dissolution process is endothermic, the dissolution reaction is favored in the reverse direction to release heat.

Therefore, the concentration of dissolved solute initially decreases with increasing temperature as more solute dissolves due to the endothermic dissolution process. However, as the temperature decreases again, the concentration of dissolved solute increases as the reverse dissolution reaction is favored and the solute precipitates out of the solution.

In summary, the concentration of dissolved solute in a saturated solution with endothermic dissolution decreases with increasing temperature and then increases again with decreasing temperature.