The mechanical properties of poly(ethylene terephthalate) (PET) fibers at temperatures above the glass transition are investigated by means of a specially constructed device. Measurements of the deformation rate and of the "dynamic" stress-strain curves of the fibers are performed in nearly isothermal regime (after initial rapid heating) in a temperature interval 100-200-degrees-C. The results reported in the present work demonstrate that the high-temperature mechanical characteristics of rapidly crystallizing polymers can be deduced to a satisfactory precision, while keeping the crystallinity development at low level. Our investigations indicate that if the high-temperature deformation is sufficiently fast, the polymer behavior is similar to the deformation at sub-T(g) temperatures. Based on this similarity, a qualitative model of the deformation in the high-temperature region is proposed. The proposed model is fundamentally equivalent to the models describing mechanical deformation of glassy polymers at temperatures below the glass transition.