Context. Very long baseline interferometry (VLBI) observations at 86 GHz (wavelength, λ = 3 mm) reach a resolution of about 50 μas, probing the collimation and acceleration regions of relativistic outflows in active galactic nuclei (AGN). The physical conditions in these regions can be studied by performing 86 GHz VLBI surveys of representative samples of compact extragalactic radio sources. Aims. To extend the statistical studies of compact extragalactic jets, a large global 86 GHz VLBI survey of 162 compact radio sources was conducted in 2010–2011 using the Global Millimeter VLBI Array (GMVA). Methods. The survey observations were made in a snapshot mode, with up to five scans per target spread over a range of hour angles in order to optimize the visibility coverage. The survey data attained a typical baseline sensitivity of 0.1 Jy and a typical image sensitivity of 5 mJy beam⁻¹, 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 observed sources and to estimate the flux densities and sizes of distinct emitting regions (components) in their jets. These estimates were used for calculating the brightness temperature (T_b) at the jet base (core) and in one or more moving regions (jet components) downstream from the core. These model-fit-based estimates of T_b were compared to the estimates of brightness temperature limits made directly from the visibility data, demonstrating a good agreement between the two methods. Results. The apparent brightness temperature estimates for the jet cores in our sample range from 2.5 × 10⁹ K to 1.3 × 10¹² K, with the mean value of 1.8 × 10¹¹ K. The apparent brightness temperature estimates for the inner jet components in our sample range from 7.0 × 10⁷ K to 4.0 × 10¹¹ K. A simple population model with a single intrinsic value of brightness temperature, T₀, is applied to reproduce the observed distribution. It yields T₀ = (3.77_−0.14^+0.10) × 10¹¹ K for the jet cores, implying that the inverse Compton losses dominate the emission. In the nearest jet components, T₀ = (1.42_−0.19^+0.16) × 10¹¹ K is found, which is slightly higher than the equipartition limit of ∼5 × 10¹⁰ K expected for these jet regions. For objects with sufficient structural detail detected, the adiabatic energy losses are shown to dominate the observed changes of brightness temperature along the jet.