Automated discovery of constitutive laws is emerging as a powerful paradigm for inverse material characterisation. Traditional modelling approaches rely on intuition-driven model formulations that may inadequately capture physical processes. While data-driven and physics-informed machine learning methods aim to address these issues, their black-box nature limits interpretability and engineering adoption. Sparse regression has emerged as a promising alternative, identifying governing laws by selecting dominant terms from candidate libraries, and has recently been extended from dynamical systems to solid mechanics with increasing applications. Herein, we extend this paradigm to the automated discovery of thermal constitutive models. We propose a framework for identifying suitable laws for transient heat conduction by constructing feature libraries for thermal conductivity and specific heat capacity. These libraries comprise combinations of diffusion-related constitutive relations inspired by a broad range of physically grounded models reported in the literature for different materials. By applying sparse regression to this rich catalogue of features, the proposed approach promotes parsimony and interpretability, isolating a minimal set of physically meaningful features that drive material response. The resulting framework offers particular impact for high-temperature applications, where material properties often exhibit strong nonlinearities and evolve due to thermal damage, phase changes, or microstructural transformations. By enabling data-driven yet interpretable identification of thermal constitutive laws, the proposed methodology has the potential to improve predictive modelling and safety assessment in applications such as fire-exposed concrete structures, energy systems, and extreme-environment engineering.