How has the chemical composition of the core of the Sun changed in the last 4.5 billion years?

The sun is about 4.5billion years old and it is considered a main sequence star, meaning its core temperature is more than 10million kelvin such that it can support fusion of hydrogen at the core to form helium. During this process, energy is released in the form of solar nutrinos as well as gamma ray photons. These gamma ray photons are are radiated from the core of the sun outward in a random walk path, colliding with other particles along the way to make its way to the surface of the sun called the photosphere. The pressure of the gas in the core is called thermal pressure and this together with electron degeneracy pressure keep the star's core from collapsing from the increasing gravitational pressure exerted by the core on the outer star material.(because the star's core becomes denser as Helium is denser than Hydrogen and so the denser core means stronger gravitational pressure).

As the gravitational pressure increases, the star contracts and gets further heated up as gravitational potential energy gets converted to thermal energy in the core, so the core temperature would keep rising increasing the rate of fusion of hydrogen in the core. This would happen for another 4-5 billion years for our sun (it is estimated) after which the temperature of the core will reach more than 100million kelvin and now the core can then support fusion of helium in the core. so helium will fuse to carbon and oxygen in the core, while the remaining hydrogen fuses to form helium. The moment helium starts to fuse in the core the sun is out of its main sequence stage.

The above gives you a basic understanding about the processes involved in the sun. So to answer the question, the suns core composition of helium has increased and its hydrogen composition has decreased over the past 4.5billion years. over the next 4-5 billion years the same chemical changes would happen in the suns core, but as explained the core temperature of the sun will keep increasing and the effect of this is that the earth will get hotter and hotter towards the end of the 4-5billion years and after that the oceans will dry up and no life can be supported anymore. So, no earthlings are unlikely to freeze over the next 4-5 billion years, they would be heated up and eventually burnt instead.