Abstract Detecting the targets of drugs and other molecules in intact cellular contexts is a major objective in drug discovery and in biology more broadly. Thermal proteome profiling (TPP) pursues this aim at proteome-wide scale by inferring target engagement from its effects on temperature-dependent protein denaturation. However, a key challenge of TPP is the statistical analysis of the measured melting curves with controlled false discovery rates at high proteome coverage and detection power. We present non-parametric analysis of response curves (NPARC), a statistical method for TPP based on functional data analysis and nonlinear regression. We evaluate NPARC on five independent TPP datasets and observe that it is able to detect subtle changes in any region of the melting curves, reliably detects the known targets, and outperforms a melting point-centric, single-parameter fitting approach in terms of specificity and sensitivity. NPARC can be combined with established analysis of variance (ANOVA) statistics and enables flexible, factorial experimental designs and replication levels. To facilitate access to a wide range of users, a freely available software implementation of NPARC is provided.