A model and a corresponding numerical procedure, based on the finite-difference method, have been developed for the prediction of buildings thermal behavior under the influence of all possible thermal loads and the "guidance" of cooling control system in conjunction with thermal comfort requirements. Using the developed procedure analyses have been conducted concerning the effects of thermostat operation mode and cooling power in terms of the time, on the total cooling energy consumption for the ideal space cooling, as well as for various usually encountered real cases, thus trying to find ways to reduce cooling energy consumption. The results lead to suggestions for energy savings up to 10%. Extensive comparisons between the ideal and various real cooling modes showed small differences in the 24-h cooling energy consumption. Because of the above finding, our detailed ideal cooling mode predictions gain considerable value and can be considered as a basis for comparison with real cases. They may also provide a good estimate of energy savings obtained if we decide to increase thermostat set point temperature. Therefore, as the extent of cooling energy saving is a priori known, one can decide if (and how much) it is worthy to increase thermostat set point temperature at the expense of thermal comfort. All results of the study, which refer to the Typical Athens Buildings during the typical Athens summer day, under the usual ranges of thermal loads, may be applicable to other regions with similar conditions.