Thermal evolution of planetary bodies is mainly controlled by its interior thermal convection and affect importantly its atmosphere and surface processes. The observations of its direct and indirect implications provides important constraints. For instance, the polygonal network found on the nitrogen glacier Sputnik Planitia (SP) on Pluto's surface (Stern et al. 2015), indicates that thermal convection operates within SP, which in turn suggests a large glacier thickness. Thermal convection, therefore, gives information that help the interpretation of planetary observations. For instance, the thickness of SP inferred by thermal convection indicates that a deep ocean is required to explain the location of SP on the equator. Thermal convection and planetary observations are therefore closely linked.
Here I present different approaches to study thermal convection and I emphasize the important link between our work and planetary observations. First, I investigate thermal convection within SP suggested by its surface polygonal network. Based on complex 3D-numerical simulations conducted for a large range of convective system, I conclude that only internal heating may produce such a surface pattern. However, there is no clearly identified source of internal heating within SP. I propose that the surface temperature variations caused by the variation in Pluto's orbit may be an appropriate source of heating. Second, I follow a parameterized approach to predict the occurrence of partial melting in exoplanets. Partial melting being necessary to maintain an atmosphere over a long period of time, which is a prerequisite for the presence of life. I found that moderate size planets are the most likely to be habitable, which show the importance of detecting Earth-size exoplanets.