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Dynamic thermal rating of overhead lines is a promising approach to increase transmission capacity by calculating weather-dependent thermal ratings (ampacities) of overhead lines in real time instead of using constant ratings. However, knowledge about ampacity is not only needed in real time but also on a day-ahead basis within network operational planning in order to assess network security. As life of humans may be endangered by inadmissible sag of overhead lines when current limits are violated there are high safety requirements concerning thermal ratings. Therefore, ampacity forecasts have to be complemented by a description of forecast uncertainty. So far, there is no method to forecast ampacities on a day-ahead basis considering uncertainty. As a comprehensive description of uncertainty is given by probability densities, this paper presents a novel method to calculate probability density functions of future ampacities based on probabilistic weather forecasts. The method's functionality is proved by application to exemplary data. [ABSTRACT FROM AUTHOR]