If asphalt pavements are exposed to cold weather conditions and high humidity for long periods of time, cracking of the pavement is an inevitable consequence. In such cases, it would be a good decision to focus on the filler material, which plays an important role in the performance variation in the hot asphalt mixtures used in the pavement. Although the use of hydrated lime as a filler material in hot asphalt mixtures is a common method frequently recommended to eliminate the adverse effects of low temperature and to keep moisture sensitivity under control in asphalt pavements, the sensitivity of the quantities of the material cannot be ignored. Therefore, in this study, an amount of filler in the mixture was replaced with hydrated lime (HL) filler additive at different rates of 0%, 1%, 2%, 3% and 4%. These asphalt briquettes, designed according to the Marshall method, have optimum asphalt contents for samples with specified HL content. In this study, where the temperature effect was examined at five different levels of −10 °C, −5 °C, 0 °C, 5 °C and 25 °C, the samples were produced in two different groups, conditioned and unconditioned, in order to examine the effect of water. The indirect tensile strength (ITS) test was applied on the produced samples. Experimental study showed that HL additive strengthened the material at low temperatures and made it more resistant to cold weather conditions and humidity. In the second part of the study, two different prediction models with varying configurations were introduced using nonlinear regression and feed-forward neural networks (FFNNs) and the best prediction performance among these was investigated. Examination of the performance measures of the prediction models indicated that ITS can be accurately predicted using both methods. As a result of comparing the developed models with the experimental data, the model provides significant contributions to the evaluation of the relationship between the ITS values obtained with the specified conditioning, temperature changes and HL contents.