Context: CARMENES is a dual-channel high-resolution spectrograph at the 3.5 m Calar Alto telescope designed to detect low-mass planets around late-type dwarfs by measuring their radial velocities (RVs). High thermal stability in both the visible (VIS) and near-infrared (NIR) channels is essential to achieve the precision required for these measurements. In particular, stabilising the NIR channel to the millikelvin level, which operates at cryogenic temperatures ( \(\sim\) 140 K), poses significant engineering challenges. Purpose: The CARMENES-PLUS project was initiated to improve the instrument’s intrinsic RV precision. In this article, we focus on the thermal stability improvements made to the NIR channel’s cooling system. Methods: The NIR cooling system was originally conceived to operate with a discontinuous flow of cryogenic nitrogen gas. As part of CARMENES-PLUS, this was upgraded to a continuous flow configuration. Additional changes included the installation of an automatic vacuum system, a proportional control valve, and a pressure regulation system. These upgrades were designed to reduce thermal fluctuations and enhance long-term stability. Results: The implemented upgrades significantly improved the intrinsic RV precision of the NIR channel. We quantified this improvement using Fabry-Pérot calibration spectra, obtaining an intrinsic RV precision of 0.67 m s\(^{-1}\) after the interventions, an improvement of nearly 2 m s\(^{-1}\). We also assessed the stability of the nightly zero points, finding a reduced scatter of 3.9 m s\(^{-1}\) post-upgrade, compared to 6.1 m s\(^{-1}\) before. For a sample of slowly rotating stars (\(v \sin i_\star \le\) 2 km s\(^{-1}\)), the median scatter decreased from 8.8 m s\(^{-1}\) to 6.7 m s\(^{-1}\) after the upgrades. Conclusions: These results demonstrate that the thermal control upgrades introduced in CARMENES-PLUS have enhanced the NIR channel’s RV performance, bringing it closer to the VIS channel’s stability and reinforcing CARMENES’s capabilities for exoplanet detection around M dwarfs.