Based on the integral representation of the semiclassical propagator of Herman and Kluk (HK), and in the limit of high temperatures, we formulate a hybrid expression for the correlation function of infrared spectroscopy. This is achieved by performing a partial linearization inside the integral over the difference of phase space variables that occurs after a twofold application of the HK propagator. A numerical case study for a coupled anharmonic oscillator shows that already for a total number of only two degrees of freedom, one of which is treated in the simplified manner, a substantial reduction of the numerical effort is achieved.