Fibers that are produced by air-gap wet-spinning are composed of cellulose, solvent and water. In the air-pp, the water evaporates at the fiber surface and this contributes to the cooling of the fiber. Here we determine the fiber temperature in the air-gap by taking into account heat conduction and convection as well as heat transfer due to evaporation. The computed temperature profiles are compared to experimental data. It is found that, close to the spinneret, water evaporates, enhancing the cooling of the fiber. At larger distances, water-vapour condenses at the fiber surface, lowering the cooling rate. The ultimate fiber temperature exceeds the temperature of the surrounding air and is determined by the balance between heat removal by convection and heat supply by condensation.