Detecting target engagement is a major challenge in drug discovery. To this end, thermal proteome profiling (TPP) offers unbiased assessment of system-wide ligand-protein interactions. However, its most sensitive assay format lacks statistical methods with false discovery rate-control. Here, we present FILIP, a functional data analysis approach and showcase its performance on several TPP-datasets probing epigenetic drugs. This leads us to identify drug off-targets which we validate in vitro.