Long-term underground cold-water cisterns had been used in old days in the hot and arid regions of Iran. These cisterns provide cold drinking water during warm seasons for local communities. In this paper, the thermal performance of an underground cold-water cistern during the withdrawal cycles in warm seasons is modeled. The cistern is located in the central region of Iran in the city of Yazd. Two approaches are used to model the heat transfer in the mentioned cistern. The first approach is meshless local Petrov–Galerkin (MLPG) method with unity test function and the second approach is artificial neural networks (ANN). For the ANN method, the multi layers perceptron (MLP) feed-forward neural network training by back propagation algorithm is used. Both methods are compared and a good agreement is observed between the MLPG and ANN results. The results show a stable thermal stratification in the cistern throughout the withdrawal cycle. The thermal stratification is linear in lower areas and exponential in upper areas. The exponential trend in the upper area is because of several factors such as: thermal exchange among the upper layers of water and the domed roof, transfer of mass and evaporation due to entry air from the wind towers.