The observations made during the Voyager 2 yby have shown that the stratosphere of Uranus and that of Neptune are warmer than expected by previous models. In addition, no seasonal variability of the thermal structure has been observed on Uranus since Voyager 2 era and signi cant subseasonal variations have been revealed on Neptune. Aims. In this paper, we evaluate different realistic heat sources that can induce suf cient heating to warm the atmosphere of these planets and we estimate the seasonal effects on the thermal structure. Methods. The seasonal radiative-convective model developed by the Laboratoire de Météorologie Dynamique was used to reproduce the thermal structure of these planets. Three hypotheses for the heating sources were explored separately: aerosol layers, a higher methane mole fraction, and thermospheric conduction. Results. Our modelling indicates that aerosols with plausible scattering properties can produce the requisite heating for Uranus, but not for Neptune. Alternatively, greater stratospheric methane abundances can provide the missing heating on both planets, but the large values needed are inconsistent with current observational constraints. In contrast, adding thermospheric conduction cannot warm the stratosphere of both planets alone. The combination of these heat sources is also investigated. In the upper troposphere of both planets, the meridional thermal structures produced by our model are found inconsistent with those retrieved from Voyager 2/IRIS data. Furthermore, our models predict seasonal variations should exist within the stratospheres of both planets while observations showed that Uranus seems to be invariant to meridional contrasts and only subseasonal temperature trends are visible on Neptune. However, a warm south pole is seen in our simulations of Neptune as observed since 2003.