[ChuckMcM]

Although you could do it with about 17km/s if you put it into a Holman transfer orbit to Venus and used a low flyby and aerobrake maneuver of Venus and that puts you into a flyby of Mercury which changes the orbital plane such that the ellipse intersects the corona.

Sad note that also limits your launch window to once every 113 years as I recall from the last time I did the math :-(.

From a technical perspective you push into an elliptical orbit that intersects Venus, you do a slight aerobreak (skim the surface of the atmosphere) to dogleg toward a Mercury intercept, and then as you pass Mercury it tightens your ellipse still further and you head out, and come back and fly through the outer corona of the Sun (which is its hottest point). At which point you're in a degenerate orbit that will go out and come back through the Sun's corona until you've been completely consumed/burned up.