Many advanced materials consist of fibers. They are used as nonwovens, fabrics, or in composite materials. Characterization of individual fibers allows us to predict resulting material properties. We present a measurement setup and analysis software to characterize individual, micrometer-sized fibers fast and reliably. The setup is based on the lockin thermography principle. Thermal diffusivity values of seven reference samples agree very well with previously reported values. We use our setup to investigate critical measurement parameters like excitation frequency, excitation power, pixel size, and fiber orientation. Our results show that fibers with subpixel diameters can be measured even if they are not aligned. However, special care has to be taken to choose an adequate excitation power. Measurements at high intensities can underestimate thermal diffusivity even though the raw data looks reasonable. By automatically measuring at different excitation powers, our setup solves this issue.