the sun isn't hot either.

comet lovejoy proved this.

Comet Lovejoy reached perihelion on 16 December 2011 at 00:17 UTC, as it passed approximately 140,000 kilometres (87,000 mi) above the Sun's surface. It was not expected to survive the encounter due to extreme conditions in the corona, such as temperatures reaching more than one million kelvins, and the exposure time of nearly an hour. However, the Solar Dynamics Observatory (SDO), as well as other Sun-monitoring spacecraft, observed the comet emerge from the corona intact. The STEREO and SOHO spacecraft continued to observe the comet as it moved away from the Sun.

[link to en.wikipedia.org]