The hybrid femtosecond∕picosecond coherent anti-Stokes Raman scattering (fs∕ps CARS) technique presents a promising alternative to either fs time-resolved or ps frequency-resolved CARS in both gas-phase thermometry and condensed-phase excited-state dynamics applications. A theoretical description of time-dependent CARS is used to examine this recently developed probe technique, and quantitative comparisons of the full time-frequency evolution show excellent accuracy in predicting the experimental vibrational CARS spectra obtained for two model systems. The interrelated time- and frequency-domain spectral signatures of gas-phase species produced by hybrid fs∕ps CARS are explored with a focus on gas-phase N2 vibrational CARS, which is commonly used as a thermometric diagnostic of combusting flows. In particular, we discuss the merits of the simple top-hat spectral filter typically used to generate the ps-duration hybrid fs∕ps CARS probe pulse, including strong discrimination against non-resonant background that often contaminates CARS signal. It is further demonstrated, via comparison with vibrational CARS results on a time-evolving solvated organic chromophore, that this top-hat probe-pulse configuration can provide improved spectral resolution, although the degree of improvement depends on the dephasing timescales of the observed molecular modes and the duration and timing of the narrowband final pulse. Additionally, we discuss the virtues of a frequency-domain Lorentzian probe-pulse lineshape and its potential for improving the hybrid fs∕ps CARS technique as a diagnostic in high-pressure gas-phase thermometry applications.