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Illuminating a silicon cantilever of an atomic force microscope with a focused laser beam creates heat that can be funneled into a nanoscale area at the apex of its tip. To characterize the heating dynamics and measure the temperature of the tip, a Raman scattering pump-and-probe method is used. It is found that at the apex of the tip the intensity of the Raman Stokes and anti-Stokes components are significantly enhanced relative to those obtained on a bulk silicon sample. Modeling the temperature rise at the tip of the cantilever by a closed-form analytical expression gives good agreement with the Raman measurements. This model can be used to design the structure of the cantilever so that the heat delivery to its tip is optimized. Such an optimized cantilever can potentially be used in high-density, heat-assisted magnetic recording, optical data storage using phase-change media and thermomechanical recording systems, for example, where nanoscale heated regions are of importance.