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In power systems with a high share of renewable feed-in, the understanding of the behavior of distributed loads and generation units and their electrical flexibility potential is of high significance. Thermal storage systems, especially in domestic heating systems, such as heat pumps (HP) or micro-CHP units, offer short- and medium-term flexibility options. The flexibility potential of individual units highly depends on the individual thermal load profile. Nevertheless, due to the high effort of measuring the thermal energy consumption of heating circuits, applicable thermal load profiles can rarely be found. As a result, this paper introduces a model for the simulation of heat demand profiles with special regard to stochastic noise. The analyzed data set consists of the measured profiles of the thermal consumption of 13 residential buildings. By means of a statistical evaluation of the heating circuits' power consumption and adaption of a stochastic differential equation, a model for the simulation of individual thermal load profiles is developed. Furthermore, the paper demonstrates the influence of stochastic thermal load profiles on the operation and the flexibility potential of CHP units