This paper presents a methodology for identifying optimal designs for air-source heat pumps suitable for domestic heating applications from the whole-energy system perspective, accounting explicitly for a trade-off between cost and efficiency, as well as for the influence of the outside air temperature during off-design operation. The work combines dedicated brazed-plate and plate-fin heat-exchanger models with compressor efficiency maps, as well as equipment costing techniques, in order to develop a comprehensive technoeconomic model of a low-temperature air-source heat pump with a single-stage-compressor, based on the vapour-compression cycle. The cost and performance predictions are validated against manufacturer data and a non-linear thermodynamic optimisation model is developed to obtain optimal component sizes for a set of competing working fluids and design conditions. The cost and off-design performance of different configurations are integrated into a whole-energy system capacity-expansion and unit-dispatch model of the UK power and heat system. The aim is to assess the system value of proposed designs, as well as the implications of their deployment on the power generation mix and total transition cost of electrifying domestic heat in the UK as a pathway towards meeting a national net-zero emission target by 2050. Refrigerant R152a appears to have the best design and off-design performance, especially compared to the commonly used R410a. The size of the heat exchangers has a major effect on heat pump performance and cost. From a wholesystem perspective, high-performance heat pumps enable a ~20 GW (~10%) reduction in the required installed power generation capacity compared to smaller-heat-exchanger, low-performance heat pumps, which in turn requires lower and more realistic power-grid expansion rates. However, it is shown that the improved performance as a result of larger heat exchangers does not compensate overall for the increased technology cost, with low-performance heat pumps being associated with the lowest system transition cost (£470 billion).