We model friction acting on the tip of an atomic force microscope as it is
dragged across a surface at nonzero temperatures. We find that stick-slip m
otion occurs and that the average frictional force follows \Inv\(2/3), wher
e v is the tip velocity. This compares well to recent experimental work, pe
rmitting the quantitative extraction of all microscopic parameters. We calc
ulate the scaled form of the average frictional force's dependence on both
temperature and tip speed as well as the form of the friction-force distrib
ution function.