I wonder if a cryogenically cooled probe could fly very fast tangentially pass the Sun and through its transition zone where the temperature drops to below 6 000 K, from millions in the corona. What maximum speed would a spacecraft achieve from the Sun's gravity and how long would it be within, say, one Solar radius of the surface?
Is the plasma in the lower corona too dense even for an ablative shield? The spacecraft could be shaped like a sphere and tumble to spread the heat. It should still be able to detect temperature, density, mass concentrations and magnetic field.