  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 towards the goal of characterising temperate
low-mass exoplanets. 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. In the present
study, we explore these aspects of mini-Neptunes using self-consistent models
of their atmospheres. We begin by exploring the effects of irradiation,
internal flux, metallicity, clouds and hazes on the atmospheric temperature
profiles and thermal emission spectra of temperate mini-Neptunes. In
particular, we investigate the impact of these properties on the
radiative-convective boundary and the thermodynamic conditions in the lower
atmosphere, which serves as the interface with the interior and/or a potential
surface. 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 H_2-rich atmospheres of such planets. We find
that observations of thermal emission with JWST/MIRI spectrophotometry can
place useful 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 planets such as GJ 3470 b. Our results underpin the
potential of temperate mini-Neptunes such as K2-18 b as promising candidates in
the search for habitable exoplanets.
