Federated Learning (FL) is a widespread and well adopted paradigm of decentralized learning that allows training one model from multiple sources without the need to directly transfer data between participating clients. Since its inception in 2015, it has been divided into numerous sub-fields that deal with application-specific issues, be it data heterogeneity or resource allocation. One such sub-field, Clustered Federated Learning (CFL), is dealing with the problem of clustering the population of clients into separate cohorts to deliver personalized models. Although few remarkable works have been published in this domain, the problem is still largely unexplored, as its basic assumption and settings are slightly different from standard FL. In this work, we present One-Shot Clustered Federated Learning (OCFL), a clustering-agnostic algorithm that can automatically detect the earliest suitable moment for clustering. Our algorithm is based on the computation of cosine similarity between gradients of the clients and a temperature measure that detects when the federated model starts to converge. We empirically evaluate our methodology by testing various one-shot clustering algorithms for over thirty different tasks on three benchmark datasets. Our experiments showcase the good performance of our approach when used to perform CFL in an automated manner without the need to adjust hyperparameters.