The properties of the glasses are not dominantly dependent on the chemical composition, temperature, and pressure but also on the thermal history. For example, electrical, thermal, optical, and mechanical properties are all known to be strongly dependent on the thermal history. Fluoride glasses have received a great deal of attention as candidate materials for an infra-red transmitting medium. A series of fluoride glasses and fibers were prepared under a nitrogen atmosphere. Thermal history effects of the fluoride glass fibers associated with the fast cooling rate employed during the fiber drawing process were discussed in terms of the glass temperatures and the fictive temperatures on the basis of the results obtained from the Differential Scanning Calorimeter (DSC) measurements of the fiber and bulk forms of the same chemical composition.