This paper addresses the challenges the policymakers face concerning the EU decarbonization and total electrification roadmaps towards the Paris Agreement set forth to solve the global warming problem within the framework of a 100% renewable heating and cooling target. A new holistic model was developed based on the Rational Exergy Management Model (REMM). This model optimally solves the energy and exergy conflicts between the benefits of using widely available, low-temperature, low-exergy waste and renewable energy sources, like solar energy, and the inability of existing heating equipment, which requires higher exergy to cope with such low temperatures. In recognition of the challenges of retrofitting existing buildings in the EU stock, most of which are more than fifty years old, this study has developed a multi-pronged solution set. The first prong is the development of heating and cooling equipment with heat pipes that may be customized for supply temperatures as low as 35 °C in heating and as high as 17 °C in cooling, by which equipment oversizing is kept minimal, compared to standard equipment like conventional radiators or fan coils. It is shown that circulating pump capacity requirements are also minimized, leading to an overall reduction of CO2 emissions responsibility in terms of both direct, avoidable, and embodied terms. In this respect, a new heat pipe radiator prototype is presented, performance analyses are given, and the results are compared with a standard radiator. Comparative results show that such a new heat pipe radiator may be less than half of the weight of the conventional radiator, which needs to be oversized three times more to operate at 35 °C below the rated capacity. The application of heat pipes in renewable energy systems with the highest energy efficiency and exergy rationality establishes the second prong of the paper. A next-generation solar photo-voltaic-thermal (PVT) panel design is aimed to maximize the solar exergy utilization and minimize the exergy destruction taking place between the heating equipment. This solar panel design has an optimum power to heat ratio at low temperatures, perfectly fitting the heat pipe radiator demand. This design eliminates the onboard circulation pump, includes a phase-changing material (PCM) layer and thermoelectric generator (TEG) units for additional power generation, all sandwiched in a single panel. As a third prong, the paper introduces an optimum district sizing algorithm for minimum CO2 emissions responsibility for low-temperature heating systems by minimizing the exergy destructions. A solar prosumer house example is given addressing the three prongs with a heat pipe radiator system, next-generation solar PVT panels on the roof, and heat piped on-site thermal energy storage (TES). Results showed that total CO2 emissions responsibility is reduced by 96.8%. The results are discussed, aiming at recommendations, especially directed to policymakers, to satisfy the Paris Agreement.