Cold super-Earths that retain their primordial, H–He-dominated atmosphere could have surfaces that are warm enough to host liquid water. This would be due to the collision-induced absorption of infrared light by hydrogen, which increases with pressure. However, the long-term potential for habitability of such planets has not been explored yet. Here we investigate the duration of this potential exotic habitability by simulating planets of different core masses, envelope masses and semi-major axes. We find that terrestrial and super-Earth planets with masses of ~1–10 M⊕ can maintain temperate surface conditions up to 5–8 Gyr at radial distances larger than ~2 au. The required envelope masses are ~10−4 M⊕ (which is 2 orders of magnitude more massive than Earth’s) but can be an order of magnitude smaller (when close-in) or larger (when far out). This result suggests that the concept of planetary habitability should be revisited and made more inclusive with respect to the classical definition.