Earth's orbital velcity is ~30km/s. So by extension, anything that comes from Earth will at least have that speed. So the probe needs to find 30km/s delta v in order to actually get close to the sun.
Long ago, playing Elite if I remember correctly, you could fly close to a star and scoop up a load of hydrogen for later resale. I'd be interested to see a graph of gas density vs tendency to melt spacecraft compared to distance from the core for a typical star.
There was a bug (or was it?) in the very PC version where by if you had fuel scoops installed, set your view to looking out the rear of the ship, flew toward a star, and ignored all the warnings on your dashboard, you could fly right through the star. If you were being chased at the time you had the additional satisfaction of watching your pursuers' ships explode as they tried to follow you in.