We report the discovery and characterisation of three transiting warm Jupiters: TIC 147027702b, TIC 245076932b, and TIC 87422071b. These systems were initially identified as transiting candidates using light curves generated from the full-frame images of the TESS mission. We confirmed the planetary nature of these objects with ground-based spectroscopic follow-up observations using FEROS and the new PLATOSpec spectrograph attached to the ESO 1.52 m telescope at the La Silla Observatory, and with ground-based photometric observations of the Observatoire Moana, Las Cumbres Observatory Global Telescope and ASTEP. From a global fit to the photometry and radial velocities, we determine that the planet TIC 147027702b has a low-eccentricity orbit (e = 0.13 ± 0.05) with a period of 44.4 days, a mass of 1.09−0.13+0.07 MJ, and a radius of 0.98 ± 0.06 RJ. TIC 245076932b has a moderately low mass of 0.51 ± 0.05 MJ, a radius of 0.97 ± 0.05 RJ, and an eccentric orbit (e = 0.43 ± 0.02) with a period of 21.6 days. TIC 87422071b has a mass of 1.29 ± 0.10 MJ, a radius of 0.97 ± 0.08 RJ, and a slightly eccentric orbit (e = 0.12 ± 0.07) with a period of 11.3 days. These well-characterised warm Jupiters expand the currently limited sample of similar gas giants and provide valuable benchmarks for testing models of giant-planet formation, migration, and tidal evolution.