How many times brighter could the stars shine without raising the temperature of space?

If my understanding is correct, the temperature of space (as defined by the temperature that a black-body will reach) has been decreasing since the big bang. It has never increased. Additionally, because of the existence of dark-energy, it seems most likely that the temperature never will increase.

Taking the large-scale universe as homogenous, how many times greater would the energy release rate of all cosmic processes have to be in order for the average temperature to hold constant against the cooling effect of dark-energy?

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Can I have an explanation for the downvote? If you don't like it, that's fine and I don't care. But one would think that it hints at some physical misunderstanding, and I am unaware of any such misunderstanding in this question. –  Alan Rominger Nov 26 '11 at 16:38
+1: Good question, but I think maybe your "Inspiration:" part caused the downvote. It really does not add much to the question and is more of a diversion into science fiction speculation that is not as appropriate for Physics.SE. I would recommend deleting that. Just IMHO... –  FrankH Nov 26 '11 at 16:50
It is worth contemplating Olber's paradox which was the argument against an infinite static universe, en.wikipedia.org/wiki/Olbers%27_paradox . In the version I was taught way back, the statement was that the temperature would also be the temperature of the stars. –  anna v Nov 26 '11 at 17:42
@annav The question of temperature of what is an important one, which is why I tried to specify blackbody temperature, but no matter which temperature you speak of the question should still make sense. I've hear people claim that thermal radiation has a specific heat of infinity, but I think that's not valid in a constant volume, or with a finite non-zero emission per unit volume. I think that simply given some mass density $kg/m^3$, power density $W/m^3$, and dark energy constant, the question should be answerable, but I do not know how, which is why I ask. –  Alan Rominger Nov 26 '11 at 17:56
the temperature in my comment is the temperature at the surface of the earth, as I remember. –  anna v Nov 26 '11 at 18:14