Although carbon nanotubes have already been demonstrated to be a promising material for bolometric photodetectors, enhancing sensitivity while maintaining the speed of operation remains a great challenge. Here, we present a holey carbon nanotube network, designed to improve the temperature coefficient of resistance for highly sensitive ultra-fast broadband bolometers. Treatment of carbon nanotube films with low-frequency oxygen plasma allows fine tuning of the electronic properties of the material. The temperature coefficient of resistance of our films is much greater than the reported values for pristine carbon nanotubes, up to -2.8% K-1 at liquid nitrogen temperature. The bolometer prototypes made from the treated films demonstrate high sensitivity over a wide IR range, a short response time, smooth spectral characteristics and a low noise level.