  The class of transiting cold Jupiters, orbiting at $\gtrsim0.5-1.0$ au, is
to-date underpopulated. Probing their atmospheric composition and physical
characteristics is particularly valuable, as it allows for direct comparisons
with the Solar System giant planets. We investigate some aspects of the synergy
between Gaia astrometry and other ground-based and space-borne programs for
detection and characterization of such companions. We carry out numerical
simulations of Gaia observations of systems with one cold transiting gas giant,
using Jovian planets around a sample of nearby low-mass stars as proxies. Using
state-of-the-art orbit fitting tools, we gauge the potential of Gaia astrometry
to predict the time of transit centre $T_c$ for the purpose of follow-up
observations to verify that the companions are indeed transiting. Typical
uncertainties on $T_c$ will be on the order of a few months, reduced to several
weeks for high astrometric signal-to-noise ratios and periods shorter than
$\sim3$ yr. We develop a framework for the combined analysis of Gaia astrometry
and radial-velocity data from representative ground-based campaigns and show
that combined orbital fits would allow to significantly reduce the transit
windows to be searched for, down to about $\pm2$ weeks ($2-\sigma$ level) in
the most favourable cases. These results are achievable with a moderate
investment of observing time ($\sim0.5$ nights per candidate, $\sim50$ nights
for the top 100 candidates), reinforcing the notion that Gaia astrometric
detections of potentially transiting cold giant planets, starting with Data
Release 4, will constitute a valuable sample worthy of synergistic follow-up
efforts with a variety of techniques.
