which way does thermal energy move when a cool breeze moves over a warm lake?

Thermal energy moves from the warm lake to the cool breeze.

Why it moves that way

Heat (thermal energy) always transfers from something warmer to something cooler until their temperatures become more equal.

In this case:

• The lake surface is warmer than the air in the cool breeze.

• When the breeze moves over the lake, the cooler air touches the warmer water.
• Energy is transferred from the warm lake water to the cooler air, warming the air and cooling the lake surface slightly.

So the thermal energy flows from the warm lake to the cool breeze , not the other way around.