Mostly speculation based on tech level. But:
To the extent temperature is an issue, energy can be used to transfer temperature from one place to another.
Maybe matter from the Sun can be physically expelled into more manageable chunks. The Sun already ejects matter naturally (though at a slow rate).
Nanotech in general (cell-like, self-replicating robots).
High energy availability with less-speculative tech like Dyson spheres.
Mostly speculation based on tech level. But:
To the extent temperature is an issue, energy can be used to transfer temperature from one place to another.
Maybe matter from the Sun can be physically expelled into more manageable chunks. The Sun already ejects matter naturally (though at a slow rate).
Nanotech in general (cell-like, self-replicating robots).
High energy availability with less-speculative tech like Dyson spheres.