Optical cooling in an all fiber system using fiber laser pumps and cooling fibers doped with rare earth ions has been investigated both theoretically and experimentally. A 2% Tm doped germanate glass was selected from glasses with different Tm concentrations 0.5, 1, 2, 3, 4, 5, 6, 8 and 10% wt for fabrication of the cooling fiber. A high efficiency, single mode Tm-doped fiber laser has been built to pump a Tm-doped fiber cooler. The cooling experiments done in a vacuum chamber show indications that cooling has occurred in the fiber. A theoretical framework to understand the nature of cooling in this laser cooling system has been developed which highlights the cooling power available as a function of various material and fiber parameters including background loss and absorption saturation effects in the cooling fiber. Cooling characteristics, with special emphasis on the fiber's saturation behavior, have been studied using theoretical models of Tm3+-doped glass (4-level models) and Tm3+ doped KLa(WO4)2 crystals (20-level model).