Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited by the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport appears more challenging. Here, we show that the shot noise generated on the edge provides a fully electrical method to probe the edge structure. In the incoherent regime, the noise falls into three topologically distinct universality classes: charge transport is always ballistic while thermal transport is either ballistic, diffusive, or "anti-ballistic". Correspondingly, the noise either vanishes, decays algebraically or is constant up to exponentially small corrections in the edge length.Electrical and thermal transport on fractional quantum Hall (FQH) edges are quantized, reflecting the bulk topological order [1][2][3]. In particular, the electrical Hall and two-terminal conductances, G H and G,are determined by the bulk filling factor ν ∈ Q. Furthermore, the thermal Hall and two-terminal conductances, G Q H and G Q , arXiv:1906.05623v1 [cond-mat.mes-hall]