Everyone is concerned about dwindling fossil fuel resources and current levels of petroleum consumption but pressure to shift to more sustainable energy sources has led to lobbyists and bigger government programs, not a better environment.

The best approach may be suited to regional conditions - some areas may use solar, some wind or geothermal, some nuclear.   There won't be a knockout technology that is a good fit  for everyone.  

What wind, solar, and geothermal power need to be useful to the masses is conversion into appropriate forms for distributing electricity. Electric power can already be distributed efficiently but conversion is necessary for use in automobiles and large-scale storage is problematic.

Keith Promislow of the Michigan State University and Brian Wetton of the University of Vancouver say the answer may be ...

PEM Fuel Cells

Polymer Electrolyte Membrane (PEM) fuel cells, also called Proton Exchange Membrane fuel cells, take hydrogen and oxygen from the air to create electricity, typically for automobiles. When pure hydrogen is used as a fuel, these fuel cells emit only heat and water as byproducts, eliminating concerns about air pollutants and greenhouse gases.  

According to the U.S. Department of Energy, fuel cells have the potential to replace the internal combustion engine in vehicles and provide power in stationary and portable power applications if they are energy-efficient, clean, and fuel-flexible.

Direct heat may not be better than indirect heat from greenhouse gases so how much heat is involved in PEM cells?  For that you need ...

Numerical modeling

PEM fuel cells are good examples of energy conversion systems that have several levels of interacting functional structures. The interactions range from proton exchange at the nanoscale level to interactions at the macroscale level among the layered media of which the cells are made.

Accurately simulating the resulting multiscale interactions requires carefully constructed mathematical models that faithfully represent the physics at the various scales. Modeling and analysis of PEM fuel cell structures, their construction, performance, and degradation also requires the development of new mathematical solutions and highly structured and highly adaptive numerical techniques.

Mathematical analysis and scientific computation will play a large role in the resolution of these important issues and as a result will affect the progress of PEM fuel cell research and development.

Article: Keith Promislow,Brian Wetton, 'PEM Fuel Cells: A Mathematical Overview', SIAM J. Appl. Math. Volume 70, Issue 2, pp. 369-409 (2009),  http://dx.doi.org/10.1137/080720802