Well let's get some numbers. A CO2 doubling is usually treated as a top-of-atmosphere imbalance of about 4 W/m^2 with fast (century delay or shorter timescale) feedbacks included. What would the comparable number be for ordinary, sensible, net-emission-free energy usage?
Well, here's a site claiming "Using 1995 figures provided by the World Bank, in that year, the world's energy consumption totaled 316 quadrillion BTUs." OK that's 316,000,000,000,000,000 = 3.16e17 BTUs = 9e16Watt-hour = 9e13 KwH = 9e13/7e9 KwH/capita-yr = 12800 KwH/capita-yr = 12800/(365*24) Kw/capita = 1.4 Kw. So the average person and all his or her support infrastructure currently burns about 1400 watts, night and day. That seems believable.
Then the world wattage is 1.4e3 * 7e9 = about 1e13 W. The area of the world is 5.1 e8 km^2 = 5.1e14 m*2. So the direct heating of existing energy is on the order of 1e13/5e14 W or about 1/20 watt per square meter. Compare this with 2 watts of anthropogenic greenhouse forcing, on its way to 4.
This is in line with what I got all the other times I worked it through, it's just verging on noticeable but is certainly not comparable to anthropogenic greenhouse forcing. Even if everyone lived at much higher US power consumption levels, this would still be a small forcing, about 1/3 W/m^2, comparable to observed solar variability.
But in the 8 July 2008 issue of EOS, whose website, proudly proclaiming its mission for the advancement "through unselfish cooperation in research, [of] the understanding of Earth and space for the benefit of humanity." doesn't make available to nonmembers, Eric Chaisson of Tufts and Harvard puts a different spin on this story. He suggests that this comfortable margin is not as comfortable as all that under conventional growth scenarios.
He points to theories that 1) economic growth is tightly coupled to energy growth and 2) economists believe healthy economic growth is at least on the order of 1%/annum sustained. Suppose we stipulate these ideas. When does non-greenhouse anthropogenic global warming become a problem? High school level computations suffice for an estimate on the order of 450 years for a global warming of 10 degrees Celsius. Higher growth rates bring that point much closer. And nothing in the assumptions allows the warming to stop there.
Accordingly, even in the total absence of an anthropogenic greenhouse effect, the world cannot sustain indefinite increases in energy use. Either the coupling of growth to energy or the growth itself will necessarily stop. Blithely ignoring the discount rate and thinking like a geophysicist, Chaisson concludes as follows:
Even acceding that the above assumptions can only be approximate, the heating consequences of energy use by any means seem unavoidable within the next millennium - a period not overly long and within a time frame of real relevance to humankind.Got that? It's a fundamental limit to growth from which there is no escape (short of escape velocity) It won't cut in soon but if none of the other ones do, this one will eventually show up. The future of the planet has fundamental limits.
More than any other single quantity, energy has fostered the changes that brought forth life, inetlligence, and civilization. Energy also now sustains society amd drives our economy, indeed grants our species untold health, wealth and security. Yet the very same energy processes that have enhanced growth also limit future growth, thereby constraining solutions to global warming. Less energy use, sometime in the relatively near future, seems vital for our continued well-being, lest Earth simply overheat.
Update: Tidal notes that this limit does not apply to earth-based renewable energy, i.e., directly or indirectly solar. The question of what fraction of that we can appropriate is not obvious to me, but the total is vast. A quick follow-up on the calculation above indicates that solar forcing (after relection) is about 4000 times human energy consumption. We appropriate a good fraction of it already for food, though.
If we assume that we can appropriate 10% of that energy effectively at most (allowing some for a biosphere, some for food production, and some for insurmountable inefficiency in the conversion process) that leaves some 8 or so doublings. At 1 % growth that is about 560 years until we run out of renewables. Still in the same ballpark as Chaisson's numbers. At 3% growth in a pure renewables scenario, we run out of sources of renewables in 180 years.