  Warm Jupiters -- defined here as planets larger than 6 Earth radii with
orbital periods of 8--200 days -- are a key missing piece in our understanding
of how planetary systems form and evolve. It is currently debated whether Warm
Jupiters form in situ, undergo disk or high eccentricity tidal migration, or
have a mixture of origin channels. These different classes of origin channels
lead to different expectations for Warm Jupiters' properties, which are
currently difficult to evaluate due to the small sample size. We take advantage
of the \TESS survey and systematically search for Warm Jupiter candidates
around main-sequence host stars brighter than the \TESS-band magnitude of 12 in
the Full-Frame Images in Year 1 of the \TESS Prime Mission data. We introduce a
catalog of 55 Warm Jupiter candidates, including 19 candidates that were not
originally released as \TESS Objects of Interest (TOIs) by the \TESS team. We
fit their \TESS light curves, characterize their eccentricities and
transit-timing variations (TTVs), and prioritize a list for ground-based
follow-up and \TESS Extended Mission observations. Using hierarchical Bayesian
modeling, we find the preliminary eccentricity distributions of our
Warm-Jupiter-candidate catalog using a Beta distribution, a Rayleigh
distribution, and a two-component Gaussian distribution as the functional forms
of the eccentricity distribution. Additional follow-up observations will be
required to clean the sample of false positives for a full statistical study,
derive the orbital solutions to break the eccentricity degeneracy, and provide
mass measurements.
