In ASDEX Upgrade, the propagation of cold pulses induced by type-I edge localized modes (ELMs) is studied using electron cyclotron emission measurements, in a dataset of plasmas with moderate triangularity. It is found that the edge safety factor or the plasma current are the main determining parameters for the inward penetration of the Te perturbations. With increasing plasma current the ELM penetration is more shallow in spite of the stronger ELMs. Estimates of the heat pulse diffusivity show that the corresponding transport is too large to be representative of the inter-ELM phase. Ergodization of the plasma edge during ELMs is a possible explanation for the observed properties of the cold pulse propagation, which is qualitatively consistent with non-linear magneto-hydro-dynamic simulations.