Ablative Rayleigh-Taylor (R-T) instability is a special feature of the acceleration phase in inertial confinement fusion (ICF). Ablation stabilizes the disturbances with small wavelength, introducing a marginal wavelength. Due to a large temperature ratio, the conduction length-scale varies strongly across the wave, and the attention is limited to the intermediate acceleration regimes for which the length-scale of the marginal wavelength is in-between the smallest and the largest conduction length-scale. The analysis is performed for a strong temperature dependence of thermal conductivity. At the leading order, the ablation front appears as a vortex sheet separating two potential flows 1, 2, and the free boundary problem takes the form of an extension of the pure R-T instability with unity Atwood number and zero surface tension. It shows also some analogies with the Kelvin-Helmholtz instability described by the Birkhoff-Rott equation. However, the hot flow of ablated matter introduces a damping at small wavelength which has a form different from the usual damping (as the surface tension for example). The nonlinear patterns are obtained by the same boundary integral method as used for revisiting the R-T instability 3. Unfortunately, a curvature singularity develops within a finite time, even though the short wavelengths are stabilised. Scaling laws are derived from numerical fitting and a self-similarity solution of the problem is exhibited close to the critical time 4. The occurrence of a curvature singularity indicates that the modifications to the inner structure of the vortex sheet can no longer be neglected. A non-local curvature effect is obtained by pushing the asymptotic analysis to the next order 5. The corresponding small pressure correction is showed to prevent the occurrence of the curvature singularity within a finite time.