Words with well-known meaning in colloquial language often make up an educational challenge when introduced as terms with formal scientific meaning. New connections must be established between the word, already constrained by existing meaning and reference, and the intended formal scientific meaning and reference. A two-dimensional semantic/semiotic analysing schema (acronym 2-D SAS) has been developed to clarify a given word/term in a structured mode both according to non-formal senses and referents and formal scientific meaning and referents. The schema is constructed on ideas from semantics, semiotics and history and philosophy of science. The approach is supposed to be a contribution to make a fine-gained analysis of the structure and dynamics of conceptual change. The role of referents and referent change in conceptual change is highlighted by analysing the character of the recurrent mix-up of the terms heat and temperature among students at different educational levels.