Recent multiple wavelength observations of sunspot umbrae are explained within the framework of an inhomogeneous, two-component model of the structure of the umbral transition region, the Wroclaw-Ondrejov model. Simple analytical expressions for the atmospheric structure in each component, and in the lower corona, are derived and the free parameters were fitted to observations of EUV emission line intensities. It is shown that the main component of the umbral transition has a shallow transition region and a deep set corona. The second 'active' component displayed a large transition region embedded in the main coronal component.The spatial filling factor of the active component was about 5-10 percent in sunspots having bright EUV plumes. For sunspots without bright EUV plumes, the spatial filling factor was more than ten times smaller. The EUV emission line intensities are compared to temperature measurements in both quiet and active sunspot regions and the results are discussed in detail.