Evidence of physical interaction with the target protein is essential in the development of chemical probes and drugs. The cellular thermal shift assay (CETSA) allows evaluation of drug binding in live cells but lacks a framework to support quantitative interpretations and comparisons with functional data. We outline an experimental platform for such analysis using human kinase p38α. Systematic variations to the assay's characteristic heat challenge demonstrate an apparent loss of compound potency with an increase in duration or temperature, in line with expectations from the literature for thermal shift assays. Importantly, data for five structurally diverse inhibitors can be quantitatively explained using a simple model of linked equilibria and published binding parameters. The platform further distinguishes between ligand mechanisms and allows for quantitative comparisons of drug binding affinities and kinetics in live cells and lysates. We believe this work has broad implications in the appropriate use of the CETSA for target and compound validation.