This study proposes a novel integrated system (IES) model to promote load distribution and thermal energy management by considering the turbulence effects, dynamic pressure fluctuations, and the nonlinear efficiency of energy conversion processes. This framework enhances the mass and energy balance equations, thus enhancing the accuracy of the hydraulic and thermal loss estimates. Further, a demand response (DR) model is also created, accounting for stochastic fluctuations in thermal and electrical demands and incorporating cross-elasticity effects. This will enable a more accurate representation of the consumer's reactions to changes in the pricing. We employ a modified particle swarm optimization (MPSO) algorithm to optimize the energy dispatch strategy. The modified version includes adjustable learning rates and changing inertia weights, which help it find solutions faster and more accurately. The algorithm successfully manages the distribution of electricity and heat energy, taking into account how energy storage works and the complexities in the conversion systems.