Heat energy doesn't "accumulate" at the surface of the liquid.
Temperature measures the average speed of the molecules, so even when the temperature is uniform throughout the liquid, some of the molecules are moving a bit faster than average and others a bit slower. At the surface of liquid, if one of the "bit faster" ones happens to moving in an upwards direction, it can escape.
The effect is to slightly cool the surface; the faster-moving molecules are more likely to escape so the average energy of the ones left behind goes down. But as you say... heat moves from areas of high temperature to lower, so as the surface cools, heat flows from the warmer interior of the liquid and eliminates the temperature differential again.