We propose a simple method of determining solvent drying rates from heat flux measurements across thin liquid films. The theory is based on quasi-steady conductive heat transport through coatings, combined with simultaneous heat and mass transfer in the gas phase. The measured evaporation rates well reproduce conventional gravimetric measurements with an uncertainty of less than 5%. Drying experiments also revealed that the proposed method is robust in systems with high levels of fluctuation and thus provides an alternative tool for monitoring drying kinetics in forced air flows.