We present results on the intrinsic brightness temperature of a sample of compact radio sources observed at 86 GHz using the Global Millimeter VLBI Array. We use the observed brightness temperatures at 86 GHz and the observed superluminal motions at 15 GHz for the sample in order to constrain the characteristic intrinsic brightness temperature of the sample. With a statistical method for studying the intrinsic brightness temperatures of innermost jet cores of compact radio sources, assuming that all sources have the same intrinsic brightness temperature and the viewing angles of their jets are around the critical value for the maximal apparent speed, we find that sources in the sample have a characteristic intrinsic brightness temperature, $T_0=4.8^{+2.6}_{-1.5}{ imes}10^9K$, which is lower than the equipartition temperature for the condition that the particle energy equals to the magnetic field energy. Our results suggest that the VLBI cores seen at 86 GHz may be representing a jet region where the magnetic field energy dominates the total energy in the jet.