While there is great interest in polymer nanofibers due to their high strength, methods to measure their time-temperature superposition (TTS) curves are lacking. The objective of this work is to demonstrate one such method and thereby to predict room temperature creep compliance over many decades of time. A complimentary measurement is also presented to estimate the associated activation energy. The experimental method is demonstrated for polyacrylonitrile (PAN) nanofibers using an on-chip surface micromachined stepper motor actuator. It is first shown that the method yields good agreement with previous room temperature measurements. Subsequently, data up to 95 degrees C, near the glass transition temperature, is presented. Time-temperature superposition master curves are then constructed, and activation energies for two narrow diameter ranges (221 +/- 27 nm and 150 +/- 9 nm) are determined. The activation energy of the 221 nm fiber agrees well with the bulk PAN value, while the 150 nm fiber is 50% larger, indicating the importance of higher chain packing and reduced chain mobility in thinner fibers. TTS curves spanning 7 (221 nm) and 9 (150 nm) decades are presented. Over this time span the creep compliance increases by a factor of approximately 10 for each. This work demonstrates a viable method to measure polymer nanofiber TTS curves from which quantitative activation energy can be determined, and from which creep compliance values over time can be predicted.