Depending on where you measure the temperature of a red giant, it can either be colder than the Sun or much hotter.
A Sun-like star may be able to sustain a habitable zone for several billion years at a distance of about two astronomical units, while it is evolving into a red giant.
Our own Sun will enter the red giant phase in about five billion years. Its outer layers will swallow Mercury and Venus and possibly Earth as it expands.
All red supergiant stars that have been detected so far rotate either slowly or extremely slowly, it can be challenging to tell if the star is spinning at all.