Warm Jupiters are ideal laboratories for testing the limitations of current tools for atmospheric studies. The cross-correlation technique is a commonly used method to investigate the atmospheres of close-in planets, leveraging their large orbital velocities to separate the spectrum of the planet from that of the star. Warm Jupiter atmospheres predominantly consist of molecular species, notably water, methane, and carbon monoxide, often accompanied by clouds and hazes muting their atmospheric features. In this study, we investigate the atmospheres of six warm Jupiters, K2-139 b, K2-329 b, TOI-3362 b, WASP-130 b, WASP-106 b, and TOI-677 b, to search for water absorption using the ESPRESSO spectrograph, reporting nondetections for all targets. These nondetections are partially attributed to planets having in-transit radial velocity changes that are typically too small (less than or similar to 15 km s-1) to distinguish between the different components (star, planet, Rossiter-McLaughlin effect, and telluric contamination), as well as the relatively weak planetary absorption lines as compared to the signal-to-noise ratio of the spectra. We simulate observations for the upcoming high-resolution spectrograph ANDES at the Extremely Large Telescope for the two favourable planets on eccentric orbits, TOI-3362 b and TOI-677 b, searching for water, carbon monoxide, and methane. We predict a significant detection of water and CO, if ANDES indeed covers the K-band, in the atmospheres of TOI-677 b and a tentative detection of water in the atmosphere of TOI-3362 b. This suggests that planets on highly eccentric orbits with favourable orbital configurations present a unique opportunity to access cooler atmospheres.