  Tapered optical fibers (nanofibers) whose diameters are smaller than the
optical wavelength are very fragile and can be easily destroyed if excessively
heated by energy dissipated from the transmitted light. We present a technique
for monitoring the nanofiber temperature using two-stage heterodyne detection.
The phase of the heterodyne output signal is determined by that of the
transmitted optical field, which, in turn, depends on the temperature through
the refractive index. From the phase data, by numerically solving the heat
exchange equations, the temperature distribution along the nanofiber is
determined. The technique is applied to the controlled heating of the nanofiber
by a laser in order to remove rubidium atoms adsorbed on its surface that
substantially degrade its transmission. Almost 90% of the nanofiber's original
transmission is recovered.
