This slows the collapse down, but it doesn't stop it. At this point ionizing hydrogen holds the surface at a constant temperature, while the contraction reduces the star's luminosity. A star evolving this way is said to be on a Hayashi track. During these early phases, the stars energy comes entirely contraction. Further contraction increases the surface temperature.
Higher mass stars deplete their cores much more quickly.
As the core runs out of hydrogen, fusion moves out to a shell around the core. Meanwhile, the helium core contracts and heats up. This heatup of the core causes the outer layers of the star to expand and the overall luminosity to go up. The star evolves up through the subgiant and giant branches. By the time He burning occurs, the core is degenerate.