Thermal property measurement of individual micro- and nano-materials has been very challenging and the development of measurement methods is crucial for the experimental investigation of microscale and nanoscale heat transfer. Here we present a noncontact frequency-domain Raman method to measure thermal diffusivity of individual 1D microfibers and nanowires without the need of knowing laser absorptivity. Cosine-wave modulated laser is used to heat the sample, while the laser-intensity-weighted spatiotemporal average temperature is simultaneously detected from the sample's Raman band shift. Transient heat conduction models under periodic heating are established and analytically solved in the frequency domain with considerations of the Gaussian laser distribution and thermal contact resistance. By varying the laser modulation frequency as well as the laser spot size, we can eliminate the laser absorptivity by a normalization technique and extract the thermal diffusivity with high sensitivity. Typically, if the thermal diffusivity is on the order of 10(-4) m(2)/s, we need to use the modulation frequencies on the order of 10 Hz to measure millimeter long microfibers, and similar to MHz frequencies to measure micrometer long nanowires. We also demonstrate that any kind of periodic laser modulation can be decomposed to a series of cosine modes and readily analyzed by this frequency-domain approach, which can greatly broaden the applications of transient Raman techniques. (C) 2019 Elsevier Ltd. All rights reserved.