<p>This work focuses on the use of sheep wool as a thermal insulating material in the building sector, as a replacement for conventional insulators. It presents the results of the experimental thermophysical characterization of three forms of wool (wool yarns, woolen tablecloths, and virgin wool), carried out using the hot-wire method, as well as a mathematical simulation based on penalized B-splines to smooth the evolution of temperature as a function of time T = f Ln (t).The scientific novelty and the original objective of this measurement technique, suitable for the geometry of wool fibers, is to avoid compression and bunching. The results show that the sheep wool has a low thermal conductivity of around 0.032–0.037 W/m.K, for densities ranging from 24.77 to 77.78&#xa0;kg/m³, and that the thermal resistance of these three forms also varies from 3.12 to 2.70 m².K/W. Sheep wool is potentially sustainable and has a low environmental impact, contributes to the energy transition, in other words, to a structural change in the way we produce and consume energy, and to sustainable development, contributing to finding solutions to the world's energy challenges in terms of global warming and the depletion of natural resources, particularly fossil fuels.</p> Graphical Abstract <p></p>