The brain processing of human natural speech is a cutting edge field of neuroscience. Non-invasive neuroimaging methods have been shown to have certain limitations when it comes to investigating cortical responses to comprehensive multi-level rapid stimuli. In this study, the temporal response function (TRF) method was employed to analyse the recorded magnetoencephalography (MEG) data of participants during the perception of Russian auditory speech. The present study employed acoustic (acoustic envelope, word and phoneme onsets) and semantic (semantic dissimilarity) predictors to reveal the response functions to each predictor changes in temporal lobe. A comparison was made between the full model MEG prediction power and the shuffled model power for each predictor. It was exclusively the acoustic envelope that demonstrated the enhanced predictive capability of the TRF model in the right hemisphere. Consequently, this work represents a pioneering contribution to the field, as it is the first to utilise TRF analysis in the context of auditory Russian speech, and a new insight into the current field of TRF speech analysis.