While this is a straightforward guess, and doesn't make any clever use of the description or hints, I think it is
The Andromeda galaxy. It spans only a few times the width of the moon in the sky, which looks small to us. It's visible with the naked eye if you're far enough away from light pollution. I'm not sure about the "longer and wider than the eye can see" part. I mean, it would span longer than our visual field if we were sufficiently close, but you could say that about anything wider than our eye.
For the hints:
It has 1 trillion stars, and we only have about 2 billion seconds in our life (we would have to count about 500 per second). Clearly it has a name. Its contains every star in the Main Sequence, which spans a the spectrum of colors. If you're in a star it's a little warm, and if you're anywhere in the empty vacuum between the stars, it gets a little chilly.