It's hard to figure out what you're getting at.
Don't know if you mean it hypothetically, turning a square wave into sinusoidal.
Are you hoping to find a way to operate in class A, without heating up the transistor?
Class A operation means the amp runs at average 50% efficiency, whatever the waveform.
There will be a certain point near the center of the operating range where power dissipation is greatest. The curve is bell-shaped. I don't know if the high point is exactly at center of operating range, or above or below.
However you mention driving the amp to clipping. When this happens you're operating it partially as a switch. Sometimes full on, sometimes full off. This reduces power dissipation. But then you don't have sinusoidal waveform coming from the transistor.
Do you mean the input is a square wave but it doesn't drive the amp to clipping? A square wave riding a DC component?