We have calculated the properties of an extra charge carrier in a polar med
ium in using a realistic self-consistent tight-binding molecular-dynamics m
ethod at finite temperature. This approach permits a quantitative, realisti
c study of polaron structure at finite temperatures; Using rutile titanium
dioxide, as an example, we report numerical data on the participation ratio
as a function of temperature. The results are consistent for a transition
from a delocalized to a localized polaron at a temperature below about 100
K. We interpret the observed localization as arising from an Anderson-like
mechanism in which the disorder associated with the thermal motion of the a
toms localizes the electron. We briefly discuss implications for transport.