I've always thought of a steam engine as definitive of the external combustion engine. There needs to be a heat exchanger for it to be defined as external combustion. Of course, the standard Otto cycle engine has a heat exchanger, often called a radiator, but that's for removing excess heat, rather than for transfering it to create power.
Of course, my understanding of such things is rudimentary at best, so this should be regarded as a combination of folklore, shamanism, urban legend and fiction. Actually, that applies to everything I write.