Our group has designed and developed a novel telecom band photon detector called the electron-injection detector. The detector provides a high avalanche-free internal-amplification and a stable excess noise factor of near unity while operating at linear-mode with low bias voltages. In our previous reports on un-isolated detectors, the large dark current of the detectors prevented long integration times in the camera. Furthermore, the bandwidth of the un-isolated detectors was in the KHz range. Recently, by changing the 3D geometry and isolating the detectors from each other, we have achieved 3 orders of magnitude reduction in dark current at same bias voltage and temperature compared to our previous results. Isolated detectors have internal dark current densities of 0.1nA/cm2 at 160 K. Furthermore, they have a bandwidth that is 4 orders of magnitude higher than the un-isolated devices. In this paper we report room temperature and low temperature characteristics of the isolated electron-injection detectors. We show that the measured optical gain displays a small dependence on temperature over our measured range down to 220 K.