We report device-level damping measurements using spin-torque driven ferromagnetic resonance on perpendicular magnetic random-access memory cells. It is shown that thermal agitation enhances the apparent damping for cells smaller than about 55 nm. The effect is fundamental and does not reflect a true damping increase. In addition to the thermal effect, it is still found that device-level damping is higher than film-level damping and increases with decreasing cell size. This is attributed to edge damage caused by device patterning.