See the below link to a paper on a small stirling cycle cogen unit developed by a NZ company in association with the Uni of Canterbury. Discusses heat transfer and mechanics of device, and you may find the references useful.
Thanks to all for the pointers. I have some ideas which fall into the general category of 'So simple someone would have done it if there wasn't something wrong with it.'
Once I'm convinced I'm not going to make a fool of myself, I'll post details so you can shoot me down!