A gas-liquid contacting apparatus and method are described, in which at least one rotor assembly including packing is arranged in a contacting chamber containing at least one stator assembly including at least one heat exchanger arranged to thermally modulate the gas-liquid contacting so that each stator assembly is operatively arranged with each stator assembly to provide gas-liquid contacting at temperatures effective for mass exchange between the gas and liquid. The rotor and stator assemblies may be of annular shape, or may be of disk shape in a stacked array of rotor assemblies alternating with stator assemblies. Such apparatus and method are usefully employed for CO2 capture from CO2-containing flue gases such as combustion effluents from power generation plants.