Here, we have introduced the residence time method for heat transfer from a body where its temperature varies with time. We consider this heat transfer problem as a model cooling process. First, we show the adaptation of the residence time method for heat transfer in general. Then, we apply this concept to the model cooling process. Further analysis is presented for the model cooling process with noises; this may be viewed as a mathematical generation of experimental data containing uncertainties and noises. The residence time method provides two characteristic time scales related to the process. However, as we show here, these time scales can be adequately estimated if the noise levels in the temperature data are low. We further discuss the possible approach to recover these parameters from the high noise level temperature data. Using these recovered time scales, one can adequately construct the temperature progression with time. Therefore, the present study may be considered a guideline for constructing the temperature progression data from noisy experimental data.