A conjugate gradient method based on an inverse algorithm is applied in this study to estimate the unknown time-dependent convection heat transfer coefficient under the varying ambient temperatures in multicoated optical fibers by reading the transient temperature measurement data at the fiber surface, when the optical fibers are subjected to transient thermal loading. No prior information is available on the functional form of the unknown convection heat transfer coefficient in the present study; thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact temperature measurements. Results show that the estimation of time-dependent convection heat transfer coefficient and transient temperature distributions can be obtained and are even effected by the varying ambient temperatures for all the test cases considered in this study.