A basic aim in molecular electronics is to understand transport through a single molecule connected to two electrodes. Substantial progress towards this goal has been made over the past decade as a result of advances in both experimental techniques and theoretical methods(1-3). Nonetheless, a fundamental and technologically important issue, currentinduced local heating of molecules(4-8), has received much less attention. Here, we report on a combined experimental and theoretical study of local heating in single molecules (6-8-and 10- alkanedithiol) covalently attached to two gold electrodes as a function of applied bias and molecular length. We find that the effective local temperature of the molecular junction first increases with applied bias, and then decreases after reaching a maximum. At fixed bias, the effective temperature decreases with increasing molecular length. These experimental findings are in agreement with hydrodynamic predictions, which include both electron - phonon and electron - electron interactions(7,9).