  We model friction acting on the tip of an atomic force microscope as it is
dragged across a surface at non-zero temperatures. We find that stick-slip
motion occurs and that the average frictional force follows $|\ln v|^{2/3}$,
where $v$ is the tip velocity. This compares well to recent experimental work
(Gnecco et al, PRL 84, 1172), permitting the quantitative extraction of all
microscopic parameters. We calculate 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 distribution function.
