Since 1967, some astronomers have intensively studied the evolution of stars similar in mass and age to our Sun. For example, Prof. Iko Iben at MIT published a ground breaking paper in 1967 ( The Astrophysical Journal, vol. 147, page 624) in which he calculated the changes in temperature, size and luminosity of stars with masses similar to our Sun. What he found out is that at the present time, 4.5 billion years after its birth, the Sun will change its luminosity by a factor of two in the next 5 billion years. In the next billion years, the amount of solar radiation reaching the Earth will increase by 8 percent.
This 8 percent increase doesn't sound like much, but if you look at a recent 1994 report by the National Academy of Science "Solar Influence on Global Climate", you will discover that a 0.1 percent increase in solar radiation causes a 'climate forcing of 0.24 watts per square meter, which leads to an increase in the mean global temperature of 0.2 degrees centigrade. From this, we can estimate that our 8 percent increase in solar radiation will cause a 16 degree increase in the mean solar temperature over the next billion years. Or 5 degrees in the next 300 million years.
If a billion years seems too long, just realize that our atmosphere will probably respond to this increase by becoming cloudier as its water vapor content climbs, and will also become richer in carbon dioxide as plant growth is stimulated, and the various terrestrial reservoirs ( oceans) begin to give-up some of their dissolved carbon dioxide. The increased greenhouse heating could make the global temperature increase somewhat higher that the simple 16 degree centigrade change due to the Sun alone.
Lets say that the mean winter temperature, now, is about 20 degrees Centigrade. A 5 degree increase in 300 million years means we are now talking about a 25 degree average winter temperature, and very few places where we can expect to see snow and ice. The average summer temperatures would be closer to 30 degrees Centigrade. If we add enhanced greenhouse heating, these estimates might easily be much higher, with the average global temperature in 300 million years looking more like 35 - 40 degrees Centigrade.
The bottom line is that in less time than it has taken higher life forms to evolve into land creatures, the Earth's biosphere may be changed by the inevitable course of the evolution of our Sun. In 300 million years or less, it may become very inhospitable for life to continue to exist on the land, and if we leave it alone, evolution may encourage life to return to the sea where the climate will be a bit more moderate.
As for humans, we may adapt to living on the land, or we may decide to leave the planet. Estimates suggest that it only takes about 5 - 10 million years to colonize the ENTIRE Milky Way galaxy, so I think we will have plenty of opportunity to survive as a species, even though Earth has become a second cousin to what Venus now looks like.
A recent review of long term climate variations among the inner planets by Michael Rampino and Ken Caldeira appearing in volume 32, of the Annual Reviews of Astronomy and Astrophysics ( 1994 page 83) suggests that an even bleaker outlook may be in store for Earth when you take into account the carbon dioxide gas in the atmosphere. The various sources and sinks are sensitive to temperature, and in the next 1.5 billion years, the global mean temperature could well exceed 80 degrees Centigrade. The evaporation of the Earth's oceans would be well underway by 1 billion years from now. We can assume that millions of years before this, Earth will have become uninhabitable. Life more complex than a bacterium has only been around for 600 million years, so it looks like we are about half way through the 'Golden Years'. To me, this is rather uncomfortably short, because it suggests that in perhaps as short as a few hundred million years, life could get very uncomfortable here!!