Why do white sauces set as they cool?

White sauces, such as béchamel, set as they cool due to the thickening agents, typically flour or cornstarch, forming a gel-like structure when heated. As the sauce cools, the starch molecules continue to absorb moisture and swell, which increases viscosity and causes the sauce to thicken further. This process is known as retrogradation, where the starch molecules realign and trap water, resulting in a firmer texture. Additionally, any fat in the sauce solidifies as it cools, contributing to the overall thickness.