Weather forecasts and warnings are the most important services provided by the meteorological profession. Forecasts are used by government and industry to protect life and property and to improve the efficiency of operations, and by individuals to plan a wide range of daily activities. Many searches have been made in weather forecasting using Artificial Neural Network (ANN) output one weather temperature degree, which give a little indicator about the weather temperature. In this paper, two weather temperatures have been forecasted using Artificial Neural Network (ANN). The design of the ANN based on two previous weather temperatures degrees (high and low), as well as, the increasing and decreasing weather temperature degree according to thermal retention. The ANN design has been applied for Baghdad city, the capital of Iraq. The training and testing used meteorological data for three years (2007-2010).