How does this relate to a star? The weight of the piston is the weight of the overlying layers. The piston doesn't sink because the gas is hot (exerts pressure). However, the radiation losses are causing the heat to slowly leak out, so that over time the piston will slowly sink. Remember, the star is in hydrostatic equilibrium throughout the contraction. Heating (the nuclear flames) at the bottom supply heat as fast as it is radiated, so star is in thermal equilibrium until it exhausts its fuel (10 Billion yrs for our sun)

In this picture, if we turn off the heat, the gas in the cylinder becomes cooler and cooler as it sinks. In this aspect stars work differently: a star becomes hotter as it cools! The difference is that a star is self-gravitating, whereas our piston gets its weight from the Earth's gravitational field.