We experimentally investigate the performance of NbTiN superconducting nanowire single photon detectors above the base temperature of a conventional Gifford-McMahon cryocooler (2.5 K). By tailoring design and thickness (8 - 13 nm) of the detectors, high performance, high operating temperature, single-photon detection from the visible to telecom wavelengths are demonstrated. At 4.3 K, a detection efficiency of 82 % at 785 nm wavelength and a timing jitter of 30 ± 0.3 ps are achieved. In addition, for 1550 nm and similar operating temperature we measured a detection efficiency as high as 64 %. Finally, we show that at temperatures up to 7 K, unity internal efficiency is maintained for the visible spectrum. Our work is particularly important to allow for the large scale implementation of superconducting single photon detectors in combination with heat sources such as free-space optical windows, cryogenic electronics, microwave sources and active optical components for complex quantum optical experiments and bio-imaging.