The same thing that happens to a star not in a Dyson sphere. It slowly radiates energy away and in the process contracts and heats up. In fact when the Earth was initially forming the Sun was only about 70% as bright as it is today.

(How liquid water could form under those conditions is still something of a mystery: https://en.wikipedia.org/wiki/Faint_young_Sun_paradox)

I really wish we would have a class K or M star as they would have a far higher life expectancy. The theorized instability in form of solar flares would probably be an acceptable compromise.

Perhaps we could just use a straw to give our sun a liposuction.