At low temperatures FeSi is a non-magnetic insulator, but becomes a metallic paramagnet for T > 300K. It has been proposed to be a Kondo insulator in which local electron correlations render a simple band structure based explanation inadequate. FeSi is unusual in that it is a 3d transition metal based material rather than f-electron based like the other Kondo insulators. We propose to characterise the spin fluctuations in FeSi at 10K, where bulk measurements and optical conductivity data imply a spin gap of about 60meV between the (heavily renormalised) valence and conduction bands, and at 300K where the evidence is that the gap has closed. We will look for the spin gap, and evidence for features qualitatitvely beyond band structure predictions, as seen in f-electron Kondo insulators.