The height distribution of hard X-ray bremsstrahlung is predicted for dissipative thermal models, involving rapid heating of many small (tearing mode) islands near the top of a magnetic arch. Emission at low energies (∊) originates mainly at high altitudes in the heated kernels themselves while high energy emission comes from the Maxwellian tail electrons escaping to the chromosphere. For a power-law distribution of kernel production temperatures, the ratio of high to low altitude emissions should vary as ∊ -2. Recent stereo occultation results (Kane et al., 1979) are consistent with this prediction for a typical size of primary dissipation kernel ≃10 km/(n/1011) for kernel density n(cm-3). The prediction should also prove a useful diagnostic for SMM data. However the small kernel size required to explain the weakness of the coronal emission demands the heating of 8 × 1036 electrons per second to above 5 keV temperatures. This is comparable to the acceleration rate above 5 keV needed in a thick target model, so that the thermal model has little energetic advantage in this event.