While I have no idea on whether the universe is infinitely large or not,
an answer to this "paradox" seems a bit obvious. Imagine you have a star,
and a senser right next to it. You would be reading a great deal of energy
from the sensor. Now, move the sensor several light years away. You would
read a great deal less energy, since most of the energy from the star would
be radiating away from the sensor. Basically, all that energy from an
infinite amount of stars would be radiating away into an infinte amount of
space. That's why our skies would be dark in an infinite universe. As for
the heating up part, <excuse me while I violate Occam's Razor (sp?)> there
could be energy abosrbing objects that create mass . . . or, the universe
can't create enough energy to fill an infinitely large void . . .
I wonder if there is anyway to show that the universe is infinitely large.
Start counting stars? <grin>