Superconducting microwave amplifiers are essential for sensitive signal readout in superconducting quantum processors. Typically based on Josephson junctions, these amplifiers require operation at milli-Kelvin temperatures to achieve quantum-limited performance. Here, we demonstrate a quantum microwave amplifier that employs radiative cooling to operate at elevated temperatures and maintain near quantum-limited added noise. This kinetic-inductance-based parametric amplifier, patterned from a single layer of relatively high-Tc NbN thin film, maintains a high gain and meanwhile enables low added noise of 1.3 quanta when operated at 1.5 K. Remarkably, this represents only a 0.2 quanta increase compared to the performance at a base temperature of 0.1 K. Based on our findings, we also discuss the practicality of such an operating scheme for various quantum applications. By uplifting the parametric amplifiers from the mixing chamber without compromising readout efficiency, this work represents an important step toward more scalable microwave quantum technologies.