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Here's a quote from the wikipedia article on sterling engines (for what it's worth):
Automotive engines
It is often claimed that the Stirling engine has too low a power/weight ratio, too high a cost, and too long a starting time for automotive applications. They also have complex and expensive heat-exchangers. A Stirling cooler must reject twice as much heat as an Otto or Diesel engine radiator. The heater must be made of stainless steel, exotic alloy or ceramic in order to support high heater temperatures needed for high power density, and to contain hydrogen gas that is often used in automotive Stirlings to maximize power. The main difficulties involved in using the Stirling engine in an automotive application are start-up time, acceleration response, shut-down time, and weight, not all of which have ready-made solutions.
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