  (abridged) Very long baseline interferometry (VLBI) observations at 86$\,$GHz
(wavelength, $\lambda = 3\,$mm) reach a resolution of about 50 $\mu$as, probing
the collimation and acceleration regions of relativistic outflows in active
galactic nuclei. To extend the statistical studies of compact extragalactic
jets, a large global 86 GHz VLBI survey of 162 radio sources was conducted in
2010-2011 using the Global Millimeter VLBI Array. The survey data attained a
typical baseline sensitivity of 0.1 Jy and a typical image sensitivity of 5
mJy/beam, providing successful detections and images for all of the survey
targets. For 138 objects, the survey provides the first ever VLBI images made
at 86 GHz. Gaussian model fitting of the visibility data was applied to
represent the structure of the sources. The Gaussian model-fit-based estimates
of brightness temperature ($T_\mathrm{b}$) at the jet base (core) and in moving
regions (jet components) downstream from the core were compared to the
estimates of $T_\mathrm{b}$ limits made directly from the visibility data,
demonstrating a good agreement between the two methods. The apparent brightness
temperature estimates for the jet cores in our sample range from $2.5 \times
10^{9}\,$K to $ 1.3\times 10^{12}\,$K. A population model with a single
intrinsic value of brightness temperature, $T_\mathrm{0}$, is applied to
reproduce the observed $T_\mathrm{b}$ distribution. It yields $T_\mathrm{0} =
(3.77^{+0.10}_{-0.14}) \times 10^{11}\,$K for the jet cores, implying that the
inverse Compton losses dominate the emission. In the jet components,
$T_\mathrm{0} =(1.42^{+0.16}_{-0.19})\times 10^{11}\,$K is found, slightly
higher than the equipartition limit of $\sim5\times 10^{10}\,$K expected for
these jet regions. For objects with sufficient structural detail detected, the
adiabatic energy losses dominate the observed changes of $T_\mathrm{b}$ along
the jet.
