Considering the extreme temperatures, I'm having a hard time trying to conceive any way of getting even close to the Sun.

If the idea is mining helium from extraterrestrial sources, I'd rather point at the gas giants. You get manageable temperatures and much lower delta-vs (which translates directly into fuel requirements).

But still, this would be an extremely expensive (i.e. unrealistic) mission, not only in terms of money, but also in terms of resources such as materials and fuel. Consider that a round trip to an outer planet does not cost twice as much as sending a probe to stay there, it costs a lot more because fuel requirements grow exponentially with delta-v. This is in addition to the fuel required to lift off from a giant planet.