Hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps CARS) is employed for quantitative gas-phase temperature measurements in combustion processes and heated flows. In this approach, ultrafast 100-fs laser pulses are used to induce vibrational and rotational transitions in N₂ and O₂, while a third spectrally narrowed picosecond pulse is used to probe the molecular response. Temporal suppression of the nonresonant contribution and elimination of collisional effects are achieved by delay of the probe pulse, while sufficient spectral resolution is maintained for frequency-domain detection and thermometry. A theoretical framework is developed to model experimental spectra by phenomenologically describing the temporal evolution of the vibrational and rotational wavepackets as a function of temperature and pressure. Interference-free, single-shot vibrational fs/ps CARS thermometry is demonstrated at 1-kHz from 1400-2400 K in a H₂-air flame, with accuracy better than 3%. A time-asymmetric exponential pulse shape is introduced to optimize nonresonant suppression with a 10³ reduction at a probe delay of 0.31 ps. Low-temperature single-shot thermometry (300-700 K) with better than 1.5% accuracy is demonstrated using a fully degenerate rotational fs/ps CARS scheme, and the influence of collision energy transfer on thermometry error is quantified at atmospheric pressure. Interference-free thermometry, without nonresonant contributions and collision-induced error, is demonstrated for the first time using rotational fs/ps CARS at room temperature and pressures from 1-15 atm. Finally, the temporal and spectral resolution of fs/ps CARS is exploited for transition-resolved time-domain measurements of N₂ and O₂ self-broadened S-branch Raman linewidths at pressures of 1-20 atm.