The SS Tsiolkovsky and USS Enterprise-D near a red giant.
A red giant is a very large, relatively cool star comprised mainly of ionized atoms. Helium is a common element found within a star of this spectral class, simply due to the fact that they have all but depleted their supply of hydrogen.
If the star is massive enough, then the helium within it will begin to fuse due to the pressure and temperatures within the star. If the star is relatively small, then it will begin to fade away.
The average temperatures of red giants are between 2500 and 3500 Kelvin.
The Xindi were building a massive weapon to destroy Earth in 2153 on one of their military outposts on Azati Prime that orbitted a red giant star. (ENT:"Azati Prime")
A binary pair of a red giant and pulsar make up the Vandor system, chosen by Paul Manheim as the site of temporal experiments because of the system's unique gravity signature. (TNG:"We'll Always Have Paris")
The SS Tsiolkovsky spent six months, from late 2363 to 2364, studying the collapse of a red giant. (TNG: "The Naked Now")