We analyze the control properties of consensus models. Starting form the link between linear multi-agent systems and the spatial semi-discretization of parabolic equations, we compare the consensus model with the heat equation. The existing techniques for PDEcontrol problems allow us to derive explicit estimates on the controllability and control cost. Our approach shows that the chain or circular network systems have the same properties as the 1D heat equation while we may extend it to the multi-dimensional orfractional type heat equations.