Rounded shapes are associated with softness and warmth, whereas Platonic solids are associated with hardness and coldness. We investigated the temperature-shape association through sensorial/conceptual qualities of geometric ice-like textured shapes. In Experiment 1, participants viewed symmetrical rotating 3D shapes (five Platonic solids—cube, tetrahedron, octahedron, icosahedron, dodecahedron; a star polyhedron and a sphere) and control shapes (naturalistic and angular), rating them in terms of liking, hardness, temperature, wetness, and texture. In Experiment 2, participants visualized ice, and selected/rated, from 22 adjectives, those corresponding to the concept of ice. In Experiment 3, for each of the shapes from Experiment 1, participants chose the most appropriate conceptual attribute from among the six attributes most frequently reported in Experiment 2. All shapes looked cold. Liking and hardness ratings were similar for the ice-sphere and the Platonic solids, with an enhanced liking and the attribution of the “beautiful” concept for starlike ice shapes. The cube was appreciated as solid and the Platonic solids as strong and bright. Self-reported introversion, extroversion, and fitness level were significantly related to the appreciation of geometric ice structures. These findings are discussed in relation to crossmodal correspondences and the role of individual differences.