The temperature coefficient of resistance of a carbon nanotube nanocomposite with the non-conductive phase-change hydrogel Poly(N-isopropylacrylamide) is studied. This nanocomposite is found to achieve the largest reported temperature coefficient of resistance, ≈−10%/°C, observed in carbon nanotube-polymer nanocomposites to date. The giant temperature coefficients of resistance results from a volume-phase-transition that is induced by the humidity present in the surrounding atmosphere and that enhances the temperature dependence of the resistivity via direct changes in the tunneling resistance that electrons experience in moving between nearby carbon nanotubes. The bolometric photoresponses of this new material are also studied. The nanocomposite's enhanced responses to temperature and humidity give it great potential for sensor applications and uncooled infrared detection.