The global ocean constitutes the largest heat buffer in the global climate system, but little is known about its past changes. The isotopic and elemental ratios of heavy noble gases (krypton and xenon), together with argon and nitrogen in trapped air from ice cores, can be used to reconstruct past mean ocean temperatures (MOTs). Here we introduce two successively developed methods to measure these parameters with a sufficient precision to provide new constraints on past changes in MOT.The air from an 800-g ice sample - containing roughly 80 mL STP air - is extracted and processed to be analyzed on two independent dual-inlet isotope ratio mass spectrometers. The primary isotope ratios (δ15 N, δ40 Ar and δ86 Kr values) are obtained with precisions in the range of 1 per meg (0.001‰) per mass unit. The three elemental ratio values δKr/N2 , δXe/N2 and δXe/Kr are obtained using sequential (non-simultaneous) peak-jumping, reaching precisions in the range of 0.1-0.3‰.The latest version of the method achieves a 30% to 50% better precision on the elemental ratios and a twofold better sample throughput than the previous one. The method development uncovered an unexpected source of artefactual gas fractionation in a closed system that is caused by adiabatic cooling and warming of gases (termed adiabatic fractionation) - a potential source of measurement artifacts in other methods.The precisions of the three elemental ratios δKr/N2 , δXe/N2 and δXe/Kr - which all contain the same MOT information - suggest smaller uncertainties for reconstructed MOTs (±0.3-0.1°C) than previous studies have attained. Due to different sensitivities of the noble gases to changes in MOT, δXe/N2 provides the best constraints on the MOT under the given precisions followed by δXe/Kr, and δKr/N2 ; however, using all of them helps to detect methodological artifacts and issues with ice quality.