We present a Raman distributed temperature sensor based on standard telecom single mode fibers and efficient polarization-independent superconducting nanowire single photon detectors. Our device shows 3 cm and 1.5 °C resolution on a 5 m fiber upon one minute integration. We show that spatial resolution is limited by the laser pulse width and not by the detection system. Moreover, for long fibers the minimum distance for a measurable temperature step change increases of around 4 cm per km length, because of chromatic dispersion at the Stokes and Anti-Stokes wavelengths. Temperature resolution is mainly affected by the drop in the laser repetition rate when long fibers are tested. On a 500 m fiber, a trade-off of 10 cm and 8 °C resolution is achieved with 3 minutes integration. Fiber-based distributed temperature sensing, combining centimetric spatial resolution with hundreds of meters sensing range, could pave the way for a new kind of applications, such as 2D and 3D temperature mapping of complex electronic devices, particles detectors, cryogenic and aerospace instrumentation.