Milton Jara Valenzuela Instituto Nacional de Matemática Pura e Aplicada (IMPA) We show that energy fluctuations on the Bernardin-Stoltz model follow an Ornstein-Uhlenbeck equation driven by a fractional Laplacian-like operator. As a consequence, we show that heat conduction in one dimension belongs to a universality class with the same exponents of the celebrated KPZ class, but with a Gaussian behavior.