The temperature dependence of $1∕f$ noise in individual semiconducting carbon nanotube (CNT) field-effect transistors is used to estimate the distribution of activation energies of the fluctuators $D(E)$ responsible for the noise. $D(E)$ shows a rise at low energy with no characteristic energy scale, and a broad peak at $\ensuremath{\sim}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The peak, responsible for the majority of noise at room temperature, cannot be due to electronic excitations, carrier number fluctuations, or structural fluctuations of the CNT, and likely results from the motion of defects in the dielectric or at the CNT-dielectric interface, or very strongly physisorbed species (binding energy $\ensuremath{\sim}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$) on the CNT or dielectric surface.