It won't, directly.

Earth, however, will likely be uninhabitable long before then (barring human actions). The Sun is growing hotter as it ages, and Earth has about another billion years left before the Sun's warming trend begins to evaporate our oceans and trigger a Venus-esque runaway greenhouse effect.

On the plus side, assuming (admittedly rather boldly) that there's any life left in the universe by then, Mars will be in the temperature range that Earth once was.

...but it still won't have a magnetic field, so it won't be able to hold on to a thick atmosphere regardless.

Mars already isn't that cold. On a warm day near Mars' equator, you could walk around in a sweater quite comfortably provided you had pressurized oxygen to breathe.

When the sun turns into a red giant it will swell to a size large enough to possibly swallow the Earth, if not be very close to it. So either our planet will also be destroyed or it will be so close that it would look like what Mercury does right now.

https://www.space.com/22471-red-giant-stars.html#section-the-future-of-the-sun

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