An analytical model, T_A(t), for the observed outside air temperature change, T_a(t), with time is developed using two components: one for the variation caused by the Earth’s movement, plus any other quasi-stationary thermodynamic effects due to industrialization; and one for the random variation caused by stochastic and/or chaotic, local environmental changes. The first component, T_R(t), describes a regular trend, expressed by periodic functions of time and constants unchanged with time. The second component, T_S, is a random, stochastic variation. For the observed outside air temperature, the analytical model of T_A(t)=T_R(t) +T_S is such as to give a statistically best approximation for the observed time period with = min. Several versions for the T_R(t) functions are defined and tested in the study for an example location for 20 years. The best model for T_R(t) t is found as a linear function with time plus a variable-coefficient Fourier series with linearly changing amplitude with time. It is found that the final analytical temperature, T_A(t), can be used not only to represent the historical daily mean temperature but also to predict the future daily mean temperature at the given location. The upper and lower boundaries give safety limits for the temperature prediction. The stochastic component identified in the model is stable and stationary. The method of model identification for T_A(t) can be used for determining input temperature functions for supporting engineering design; or for an unbiased scientific inquiry of temperature change with time in climate studies.