Naturalism entails that any predictions regarding the future must be based on established science and accurate historical evidence of past trends. It must also consider the evident course of current technologies, since the future will be largely decided by the decisions humans make and the technologies they develop to realize their plans and ambitions.
First is cosmology. We know a great deal now about the likely future evolution of the universe. Certainly within a few billion years the earth will be consumed by the sun, although we have the means even now to escape this fate, using space travel to live elsewhere. But it's very likely that countless trillions of years from now all the stars in the universe will have burned out, and the remaining debris will have collapsed into black holes, which will evaporate after many more trillions of years, leaving the universe a sea of random electromagnetic noise and scattered subatomic particles. However, due to the Third Law of Thermodynamics, it will take infinite time for all the available energy in the universe to become unusable, which means human technologies will always be able to exploit remaining heat differentials to produce energy to sustain civilizations for eternity. However, this will require human civilization to have survived that long.
Which leads us to the real question: How will human civilization fare over the coming millions of years, since there is no god to save us and we are all left to our own devices? Judging from the past, and even considering the unexaggerated realities of destructive technologies (like nuclear bombs and global warming) and natural phenomena (like asteroids and supernovas), it seems highly likely that human civilization will continue indefinitely. This is not guaranteed, as improbable misfortunes can overcome us. And it won't be free of cycles of progress and decline, as failures and catastrophes set us back and we must recover. But in the long run, the odds are good we will overcome all obstacles and threats with new technologies, and continue doing so for all eternity. This will especially be true if we improve our moral cooperation with reasonable philosophies like secular humanism, working together to create a good society, rather than destroy ourselves in fits of barbaric religious violence and madness. It will also help if we increasingly learn to work for the common good rather than blindly ruin the earth in pursuit of mere profit and greed.
If we do this, within a thousand years human technology will be so advanced we will be able to create and live inside computer simulated worlds as real as our present world. Countless individuals and groups will each design their own universes, and individuals will be able to live in any of those worlds they want to, even hopping from one to the next if they grow to dislike the one they first choose. Everyone will live forever, and because these new worlds will be intelligently designed (and constantly subject to improvement in design) and because we will get to choose which one to live in (even creating our own if we want), they will be far better worlds than the one we now live in. Though none is likely to be absolutely perfect, there will certainly be many to choose from that we could fairly call paradise.
Of course, even if the human race goes extinct (either because of our own immoral stupidity or some unstoppable accident of nature), the odds are extremely good that there are many other civilizations in this universe, and since risk will be distributed among them all, it is nearly certain at least one intelligent species, somewhere in this universe, will endure for all eternity, creating and enjoying the virtual utopia just described.