In this talk we will present a mechanism whereby diffusion causes the onset of stable oscillations in a simple nonlinear scalar heat equation that can be interpreted as a single-input single-output feedback control system. We show that the trivial solution solution looses its stability due to a Hopf bifurcation. The discussion includes a detailed spectral analysis of the non self-adjoint linearization, which canbe thought of as a rank 1 non-symmetric perturbation of the Laplacian