A black felt hat, when seen in the near-infrared, is quite reflective.
This was taken with the Canon S300, with no IR-pass filter. It shows a combination of visible light and near-infrared, since the IR-block in the camera was removed. My lighting source was halogen incandescent, a rich source of near-IR light. The black felt is very light-colored in the near-infrared, as bright as the visible tan sweat band, and we see it is even more reflective the further into the IR we go. The blue channel is a combination of visible blue (on a black hat there is none) and infrared radiation leaking through the blue filters on the CCD. Most bandpass color filters also pass light of wavelength double of their design: so blue filters, with a peak transmission of about 450nm, will transmit at 900nm as well.