We report the discovery and orbital characterization of three new transiting warm giant planets. These systems were initially identified as presenting single-transit events in the light curves generated from the full-frame images of the Transiting Exoplanet Survey Satellite. Follow-up radial velocity measurements and additional light curves were used to determine the orbital periods and confirm the planetary nature of the candidates. The planets orbit slightly metal-rich late F- and early G-type stars. We find that TOI 4406b has a mass of M P = 0.30 ± 0.04 M J, a radius of R P = 1.00 ± 0.02 R J, and a low-eccentricity orbit (e = 0.15 ± 0.05) with a period of P = 30.08364 ±0.00005 days. TOI 2338b has a mass of M P = 5.98 ± 0.20 M J, a radius of R P = 1.00 ± 0.01 R J, and a highly eccentric orbit (e = 0.676 ± 0.002) with a period of P = 22.65398 ± 0.00002 days. Finally, TOI 2589b has a mass of M P = 3.50 ± 0.10 M J, a radius of R P = 1.08 ± 0.03 R J, and an eccentric orbit (e = 0.522 ± 0.006) with a period of P = 61.6277 ± 0.0002 days. TOI 4406b and TOI 2338b are enriched in metals compared to their host stars, while the structure of TOI 2589b is consistent with having similar metal enrichment to its host star. *Based on observations collected at the European Organization for Astronomical Research in the Southern Hemisphere under ESO programmes 0104.C-0413, 106.21ER.001, and 108.22A8.001 and MPG programmes 0103.A-9008 and 0104.A-9007.