The temperature dependence of peak widths in high resolution angle-resolved photoelectron spectroscopy from quantum well states in ultra thin Ag films on V(100) has been used to determine the electron-phonon coupling constant, lambda, for films of thickness 1-8 layers. A strong oscillatory variation in coupling strength is observed as a function of film thickness, peaking at a 2 layer film for which lambda~1. A simple theory incorporating interaction of the photo-hole with the thermal vibrations of the potential step at the adlayer-vacuum interface is shown to reproduce the main features of these results.