Atmospheric observations of mini-Neptunes orbiting M-dwarfs are beginning to provide constraints on their chemical and thermal properties, while also providing clues about their interiors and potential surfaces. With their relatively large scale heights and large planet-star contrasts, mini-Neptunes are currently ideal targets for atmospheric characterisation in the low-mass regime. Understanding the thermal structures and spectral appearances of mini-Neptunes is important to understand various aspects of their atmospheres, including radiative/convective energy transport, boundary conditions for the interior, and their potential habitability. We explore these aspects of mini-Neptunes using self-consistent atmospheric models to explore the effects of irradiation, internal flux, metallicity, clouds and hazes. Building on recent suggestions of habitability of the mini-Neptune K2-18 b, we find a range of physically-motivated atmospheric conditions that allow for liquid water under the H2-rich atmospheres of such planets. We find that observations of thermal emission with JWST/MIRI spectrophotometry can place important constraints on the habitability of temperate mini-Neptunes such as K2-18 b, and provide more detailed constraints on the chemical and thermal properties of warmer Neptunes/mini-Neptunes such as GJ 3470 b. These results underpin the potential of temperate mini-Neptunes such as K2-18 b as promising candidates in the search for habitable exoplanets.