Why Is Space Cold If There Are So Many Stars?

Space is filled with countless stars, all of which radiate enormous amounts of heat. These stars are tens of thousands of times bigger than our own sun. Still, space is considered to be cold. Why is that? If there are so many hot burning stars in space, why is space so cold? From a purely technical standpoint, it’s not fair to say that space is cold in itself. Because technically, space is just a vacuum, and vacuum doesn't have a temperature of its own. It’s the objects in space that become cold in due time because they continuously lose heat due to radiation. In addition to that, it’s not like all these stars are clumped up together. These stars are extremely hot, sure, but they are so far apart and have so much space between them that it’s simply impossible for them to heat up space. It is totally different from what you see when you look up at the night sky. In a nutshell, space is cold, despite having so many stars, because space contains such an incomprehensibly large amount of nothingness.