Noodles wrote:
But what if you could take the heat out and convert it into other useful forms of energy? As (I think) I mentioned, there already exists the technology to take heat from the ground and the sea and convert it to a more useful source of energy, if we could expand this technology to be used on a much larger scale, we could be onto something.
Short answer: Yes we have more energy, but that won't help.
Ah the second law of thermodynamics. Okay here's the deal:
Heat spontaneously travels from high temperature places to low temperature places. It's like water sliding downhill. In the process, we can persuade some of it to do work for us. Imagine the water turning a giant waterwheel.
The efficiency of the process is defined to be the amount of useful work done (the waterwheel turning) divided by the heat energy from the hot place required to do so. (The rest of the energy which does not go into useful work goes directly, as heat, into the cold place. Of course the work will eventually turn into heat as well, and most of this will go into the cold place).
The maximum theoretical efficiency of a heat engine is given by the Carnot cycle. No real engines undergo the Carnot cycle. However, the efficiencies parallel the Carnot efficiency, and the equation for Carnot efficiency is simple. It is: one minus the quantity: (the temperature of the cold place divided by the temperature of the hot place) e = 1 - (T_c/T_h). (all temperatures in Kelvin).
The *cold* place where our engines put the heat is the atmosphere. Making that hotter decreases efficiency (although not by much).
Geothermal energy takes heat from the (hotter) deep places in the Earth and puts it into the (relatively colder) atmosphere. Again, making the atmosphere hotter makes this process less efficient (although, again not by so much - although this is much more effected then car engines).
Noodles: if you would care to post details I can look into whatever you are thinking about in further detail. As it stands now, I simply cannot imagine any way global warming would help.
Side note: Although there are places which will cool under global climate models, such changes are on large length scales and any kind of heat engine works quite locally: both to the end user of the useful work and the hot/cold places.