How likely is it both scientifically and medically that Frank Poole could have been found in space and revived as in 3001: The Final Odyssey, 1000 years after Hal jettisoned his body from the Discovery?
Actually, it is worse than what Zypher said. Space doesn't have anything for your body to lose heat through, so you only lose heat slowly through radiation. The core body temperature of Frank would have been sufficient for long enough for the bacteria in his gut to have ate their way through most of his body. Spreading outward and consuming his body. He would swell, then release a stream of putrid fluid into space.
He would have shot around like a water balloon with the end untied. This destabilization would have likely lead him out of any chart-able orbit, which would have been tenuous anyway, as he probably would have floated along with the ship and burned up in Jupiter's atmosphere. Or would have been slingshot into the sun or out of the solar system as a meat version of the Voyager probe.
Only harder to find, since his trajectory would be incalculable. So it would be a sphere around the solar system of roughly 500,000,000,000 miles. (If Jupiter didn't impart any additional speed to his body, and Discovery was traveling at roughly 50,000 MPH.)
I had way too much fun writing that.
Scientifically and medically, Frank Poole had no chance of survival. Space is not a cryogenic freezer. In fact due to the vacuum your body would start outgassing, and your cells would be frozen in a crystalline structure that would do massive damage both as they froze and as they thawed. Even if you are in a space suit, you would eventually be subject to these issues - you would just survive a little longer until the suit's batteries/electronics/seals failed.
Given what the others have said, i still think it would be possible to revive him, assuming you could find his body and it was relatively intact.
In a thousand years from now, assuming there isn't some huge mega-disaster that sets us back to the stone-age, think how far we will have progressed. Just consider nano-technology alone.
Even if the dna in his body is badly degraded, you could take bits and pieces of it and then assemble a whole. Using nano-robots you could either have them physically go in and repair each dna strand, and then repair each cell. Or, using the whole dna strand, grow a new body. The real question is the brain. I know the brain cells would all be trashed - destroyed by freezing and then desiccated. But maybe that's not that important, as long as you can still map out the individual connections. I'm not sure how likely that would be since when the cells freeze and dry out, i'm sure some/all of those connections are going to be broken and it might not be possible to piece them back together.
So to me, his body/dna is almost irrelevant. I'm thinking we could repair it and/or grow him a new one pretty easily by that point in the future. To me it all comes down to the brain. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2742633/ That doesn't really answer the question although it does lend some evidence that structures in the brain can be preserved after death.
http://www.alcor.org/Library/html/braincryopreservation1.html And that one is even more encouraging, although of course that's talking about freezing under controlled and optimal conditions. But it at least lends some support that it's possible to freeze the brain and maintain the structures. A 1000 years in the future i dont think it'll matter if the cells themselves are all basically destroyed. You can use nano-robots to repair them. I think it just matters if you can still map out the individual neural connections. If you can do that, then i think you could revive him.