## 1 Introduction  
Residential heating is a significant source of greenhouse gas emissions in Europe, where cold winters and high standards of comfort drive a substantial demand for heating. Across the continent, homes are primarily heated by burning fossil fuels, with natural gas, oil, and coal accounting for the majority of the energy used in household heating systems. This widespread reliance on fossil fuels has made residential heating one of the leading contributors to carbon dioxide (CO\({}_{2}\)) and other greenhouse gas emissions in Europe, directly impacting air quality and contributing to climate change. According to recent estimates, the residential sector is responsible for nearly 30% of Europe's total energy consumption, with heating comprising the vast majority of this demand, and residential heating alone produces approximately 12% of the European Union's total CO\({}_{2}\) emissions [1], a figure that fluctuates depending on seasonal temperatures and energy sources. Countries with colder climates, such as those in Northern and Eastern Europe, often exhibit even higher emissions due to longer heating periods and lower average temperatures. In the United States, buildings account for approximately 39% of all primary energy consumption and 74% of all electricity consumption [2]. Thermal end uses, including space conditioning, water heating, and refrigeration, account for approximately 50% of building energy demand and are projected to increase in the years ahead. The adoption of aerothermal and geothermal heating systems in Europe is proving to be an effective strategy to reduce greenhouse gas emissions from the residential sector. Unlike conventional fossil fuel-based heating, aerothermal and geothermal systems extract renewable heat from the air or ground, greatly reducing direct CO\({}_{2}\) emissions. Studies estimate that replacing fossil fuel heating systems with heat pumps (which include both aerothermal and geothermal technologies) could cut emissions by up to 70-80% per household. Across Europe, approximately 20 million heat pumps were installed by 2022 [3], helping to replace a portion of the emissions-heavy natural gas and oil heating systems. The European Heat Pump Association (EHPA) reports that these installations are already saving about 50 million tons of CO\({}_{2}\) annually [4]. As part of the European Green Deal, the EU aims to accelerate this shift, with projections indicating that heat pumps could power up to 40% of Europe's residential heating demand by 2030 [5]. This large-scale transition is essential for Europe to reach its net-zero emissions targets by 2050, as heat pumps not only reduce emissions directly but also operate more efficiently when paired with renewable electricity sources  
As energy systems evolve toward greater sustainability, there is growing interest in leveraging the thermal storage capacity of buildings to reduce energy consumption and shift demand patterns. Thermal energy storage (TES) is a crucial enabling technology for the large-scale deployment of renewable energy, facilitating the decarbonization of thermal end uses, including refrigeration, water heating, and space heating and cooling, and the transition to a decarbonized building stock and energy system by 2050. A variety of thermal storage solutions are available, which permit the storage of excess thermal energy or heat for subsequent utilization at a more opportune time, whether that is hours or even days later. Thus, there are several investigations in the field of advanced thermal storage materials. For example, reference [6] investigates new composites materials, and reference [7] presents a novel approach to encapsulate salt hydrate. In the field of thermal energy storage projects related to envelope systems, for example, reference [8] presents an active thermally anisotropic building envelope that redistributes thermal loads in response to weather conditions and building energy demand.