In a few billion years, the long-term evolution of the Sun will have a significant impact on the climate and temperature on Earth. As the Sun exhausts its hydrogen fuel in its core, it will enter a phase known as the red giant phase. During this phase, the Sun will expand in size and become much brighter.
As the Sun expands, it will likely engulf the inner planets, including Earth. The exact fate of Earth is uncertain, but it is expected that our planet will be swallowed by the Sun's outer layers and cease to exist as we know it.
However, if we consider a scenario where Earth somehow survives this engulfment, it would be left in a significantly altered state. The Sun's increased brightness and size would lead to a substantial increase in solar radiation reaching Earth, causing a significant rise in temperatures.
So, rather than getting colder, the Earth would experience extreme heating due to the expanding Sun in a few billion years. It's important to note that this is a general prediction based on our current understanding of stellar evolution, and further research may provide more accurate insights in the future.