We propose to use a Fabry-Perot interferometer (FPI) in a pure rotational Raman lidar to isolate return signals that are due to pure rotational Raman scattering from atmospheric nitrogen against the sky background. The main idea of this instrumental approach is that a FPI is applied as a frequency comb filter with the transmission peaks accurately matched to a comb of practically equidistant lines of a pure rotational Raman spectrum (PRRS) of nitrogen molecules. Thus a matched FPI transmission comb cuts out the spectrally continuous sky background light from the spectral gaps between the PRRS lines of nitrogen molecules while it is transparent to light within narrow spectral intervals about these lines. As the width of the spectral gaps between the lines of the PRRS of nitrogen molecules is -114 times the width of an individual spectral line, cutting out of the sky background from these gaps drastically improves the signal-to-background ratio of the pure rotational Raman lidar returns. This application of the FPI enables one to achieve daytime temperature profiling in the atmosphere with a pure rotational Raman lidar in the visible and near-UV spectral regions. We present an analysis of application of the FPI to filtering out the pure rotational Raman lidar returns against the solar background. To demonstrate the feasibility of the approach proposed, we present temperature profiles acquired during a whole-day measurement session in which a Raman lidar equipped with a FPI was used. For comparison, temperature profiles acquired with Vaisala radiosondes launched from the measurement site are also presented.