It is important to understand how completely unsettled the phylogeny of this taxonomic region is. It is not clear that either the Lepospondyls or the Temnospondyls are legitimate taxa, much less who belongs in these groups, or what their relationships might be with modern amphibians , with Amniotes , or with each other. However, precisely because the area is so unsettled, the traditional nomenclature is important even if it is probably misleading.
Cladistic definitions are much more precise and, at least theoretically, testable.
However, there is no consensus on how to apply them at the moment. The classical definition of a Temnospondyl involved vertebral characters. Actually, the intercentrum of Eryops is not all that well developed, even compared to Ichthyostega . Nevertheless, Eryops is the archetype around which the idea of a Temnospondyl revolves. Like most Carboniferous and Permian Tetrapods, Eryops is a cipher.