Could thermocoupling be used to increase gas mileage?

It is my understanding that a car engine is inefficient in terms of fuel to actual kinetic energy output. I was wondering if it would be possible to harness all the heat by-product to charge the battery. I have no idea where one would get ahold of a thermopile capable of actually making a difference, but it seems logical to me. I think the output would be DC; would that mean it could be hooked up directly to the battery? If this is the case, it seems like a really simple method to improve efficiency.

What do you think? Does this seem plausible or is it not as simple as I am making it out to be?

Thanks for any input.

First of all, a turbocharger does this, to a limited extent. It reclaims a small portion of the exhaust's thermal expansion energy for conversion into mechanical work.

A few years ago I read an article in Car and Driver magazine stating that BMW was developing thermal energy reclamation systems as an alternative to the gas/electric hybrid. As I recall, waste heat from the cooling system and exhaust were to heat and expand a medium to provide mechanical work, a bit like a steam engine does.
I have not come across anything about this since then, though.

Absolutely. You can purchase thermoelectric generators to extract waste heat from the exhaust and generate electricity. A quick search of the subject shows a nice little site that sells various modules...albeit pricey. None made specifically for exhausts, but appears it could be adapted.

http://www.tegpower.com/products.html

The only trick would be integrating it with your vehicle's battery charging system so that it doesn't overcharge your battery bank or compete with the alternator. But yes, it is possible.