http://www.solarviews.com/eng/sun.htm

First pargraph deals with the topic:

"The Sun is the most prominent feature in our solar system. It is the largest object and contains approximately 98% of the total solar system mass. One hundred and nine Earths would be required to fit across the Sun's disk, and its interior could hold over 1.3 million Earths. The Sun's outer visible layer is called the photosphere and has a temperature of 6,000°C (11,000°F). This layer has a mottled appearance due to the turbulent eruptions of energy at the surface. "

I think that for the breaf period of time, that the crab creates those temperatures, the crab would survive them.

-Aaron