We present a new method for studying the intrinsic brightness temperatures of the parsec-scale jet cores of active galactic nuclei (AGNs). Our method uses observed superluminal motions and observed brightness temperatures for a large sample of AGNs to constrain the characteristic intrinsic brightness temperature of the sample as a whole. To study changes in intrinsic brightness temperature, we assume that the Doppler factors of individual jets are constant in time, as justified by their relatively small changes in observed flux density. We find that in their median-low brightness temperature state, the sources in our sample have a narrow range of intrinsic brightness temperatures centered on a characteristic temperature, Tint_~ 3 × 10 to the 10th K, which is close to the value expected for equipartition, when the energy in the radiating particles equals the energy stored in the magnetic fields. However, in their maximum brightness state, we find that sources in our sample have a characteristic intrinsic brightness temperature greater than 2 × 10 to the 11th K, which is well in excess of the equipartition temperature. In this state, we estimate that the energy in radiating particles exceeds the energy in the magnetic field by a factor of ~ 10 to the 5th. We suggest that the excess of particle energy when sources are in their maximum brightness state is due to injection or acceleration of particles at the base of the jet. Our results suggest that the common method of estimating jet Doppler factors by using a single measurement of observed brightness temperature, the assumption of equipartition, or both may lead to large scatter or systematic errors in the derived values.