  We investigate the superfluid behavior of a Bose-Einstein condensate of
$^6$Li molecules. In the experiment by Weimer et al., Phys. Rev. Lett. 114,
095301 (2015) a condensate is stirred by a weak, red-detuned laser beam along a
circular path around the trap center. The rate of induced heating increases
steeply above a velocity $v_c$, which we define as the critical velocity. Below
this velocity, the moving beam creates almost no heating. In this paper, we
demonstrate a quantitative understanding of the critical velocity. Using both
numerical and analytical methods, we identify the non-zero temperature, the
circular motion of the stirrer, and the density profile of the cloud as key
factors influencing the magnitude of $v_c$. A direct comparison to the
experimental data shows excellent agreement.
