Fullerene peapods, which are carbon nanotubes encapsulating fullerene molecules, can offer enhanced functionality with respect to empty nanotubes. Their prospective applications include, for example, data storage devices, single-electron transistors and spin-qubit arrays for quantum computing. However, the present incomplete understanding of how a nanotube is affected by entrapped fullerenes is an obstacle for peapods to reach their full potential in nanoscale electronic applications. In this paper, we investigate the effect of C(60) fullerenes on low-temperature electron transport through peapod quantum dots. Compared with empty nanotubes, we find an abnormal temperature dependence of Coulomb blockade oscillations, indicating the presence of a nanoelectromechanical coupling between electronic states of the nanotube and mechanical vibrations of fullerenes. This provides a method to detect the C(60) presence and to probe the interplay between electrical and mechanical excitations in peapods, which thus emerge as a new class of nanoelectromechanical systems.