Here, we present the first systematic study on the temperature dependence of the extension of the superconducting proximity effect in a 1-2 atomic layer thin metallic film, surrounding a superconducting Pb island. Scanning tunneling microscopy/spectroscopy (STM/STS) measurements reveal the spatial variation of the local density of state on the film from 0.38 up to 1.8 K. In this temperature range the superconductivity of the island is almost unaffected and shows a constant gap of a 1.20 ± 0.03 meV. Using a superconducting Nb-tip a constant value of the proximity length of 17 ± 3 nm at 0.38 and 1.8 K is found. In contrast, experiments with a normal conductive W-tip indicate an apparent decrease of the proximity length with increasing temperature. This result is ascribed to the thermal broadening of the occupation of states of the tip, and it does not reflect an intrinsic temperature dependence of the proximity length. Our tunneling spectroscopy experiments shed fresh light on the fundamental issue of the temperature dependence of the proximity effect for atomic monolayers, where the intrinsic temperature dependence of the proximity effect is comparably weak.